Copyright

by

Rene Hartke

2004

Characterization, application and improvement of a

laser driven cluster fusion neutron source

by

Rene Hartke

Thesis

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Master of Arts

The University of Texas at Austin

August 2004

Characterization, application and improvement of a

laser driven cluster fusion neutron source

Approved bySupervising Committee:

Acknowledgments

For the work presented in this thesis I was supported by many people to all

of whom I am deeply grateful. I have benefited from the scientific input and the

helpful attitude of an amazing work group and other collaborators.

First of all I want to thank Todd Ditmire. He gave me some great insights

into high intensity laser matter interactions and other things. For my work he

provided great physical resources. Furthermore the outstanding atmosphere in the

work group is the effort of his supervising skills.

Next I want to thank many people I have had the oppertunity to work with

in the lab. Federico Bursgens, Dan Symes, Gilliss Dyer, Aaron Edens, Will Grigsby,

Greg Hays and Jens Osterhoff have taught me a great deal about laser treatment

and have helped me to improve my laboratory skills. I also want to thank Matthias

Hohenberger, Rainer Horlein and Alexander Maltsev for some nice discussions about

the theoretical background. Furthermore I want to thank Sean Keely for his assis-

tance with the setup of the high voltage circuit. All those guys not only have helped

me a lot, but also gave me a very enjoyable time.

I also want to thank Roger Bengtson and Keith Carter who provided me

with high voltage parts and great suggestions for high voltage and vacuum related

problems. In addition to that Roger Bengtson was so kind to act as the co-reader

for my thesis.

I am very grateful to my parents and my sister who encouraged me to study

iv

abroad. Since I can remember I could always count on their support and motivation.

For this and many other things I owe a great debt to them.

Rene Hartke

The University of Texas at Austin

August 2004

v

Characterization, application and improvement of a

laser driven cluster fusion neutron source

Rene Hartke, M.A.

The University of Texas at Austin, 2004

Supervisor: Todd Ditmire

The explosion of deuterated clusters heated by ultra short, high intense laser

pulses provides ions with sufficient energy to undergo fusion reactions. Based on

this mechanism monochromatic dd-fusion neutrons can be produced by illuminating

deuterium clusters with a high intensity laser. For the work presented in this thesis

we employed such a cluster fusion neutron source. The clusters from a cryogenically

cooled gas jet were heated with a femtosecond, terawatt class Ti:sapphire laser.

The results presented in this thesis fall into three categories. First general

features of the neutron source will be discussed including the energy dependence and

the angular dependence of the neutron source. Then as a first application of the

source the calibration of a neutron detector for single shot dd-fusion experiments

will be presented. Finally magnetic confinement as a method for increasing the

neutron yield will be discussed.

vi

Contents

Acknowledgments iv

Abstract vi

List of Figures x

Chapter 1 Introduction 1

Chapter 2 Laser Cluster Interactions 6

2.1 The Ponderomotive Potential . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Ionization Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Multiphoton Ionization . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Tunnel Ionization . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.3 Barrier Suppression Ionization . . . . . . . . . . . . . . . . . 8

2.2.4 The Keldysh Parameter . . . . . . . . . . . . . . . . . . . . . 10

2.3 Plasma Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.1 Above Threshold Ionization (ATI) . . . . . . . . . . . . . . . 11

2.3.2 Collisional Heating . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Cluster Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Requirements and Simplifying Assumptions for

Plasma Treatment of Clusters . . . . . . . . . . . . . . . . . . . . . . 14

vii

2.6 Cluster Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6.1 Cluster Expansion . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6.2 Ion Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.7 Neutron Yield Calculations . . . . . . . . . . . . . . . . . . . . . . . 19

2.8 Expected Angular Distribution . . . . . . . . . . . . . . . . . . . . . 24

Chapter 3 Apparatus for Cluster Experiments 27

3.1 The Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 The Target Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Cluster Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Chapter 4 Characteristics of the Cluster Neutron Source 35

4.1 Cluster Size Measurements . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Time of Flight Histograms . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 Pressure Dependance of the Neutron Yield . . . . . . . . . . . . . . . 39

4.4 Energy Dependance of the Neutron Yield . . . . . . . . . . . . . . . 40

4.5 Polarization Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.6 Angular Distribution of the Neutron Yield . . . . . . . . . . . . . . . 43

4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Chapter 5 Calibration of a Neutron Detector 47

5.1 The Sandia Z Accelerator . . . . . . . . . . . . . . . . . . . . . . . . 47

5.2 The Neutron Detector on Z . . . . . . . . . . . . . . . . . . . . . . . 50

5.3 Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Chapter 6 Pulsed Magnetic Mirror Confinement of the Plasma Fila-

ment 58

viii

6.1 Confinement of the Plasma Filament . . . . . . . . . . . . . . . . . . 58

6.2 Creating a High Magnetic Field . . . . . . . . . . . . . . . . . . . . . 61

6.2.1 Design of the Circuit . . . . . . . . . . . . . . . . . . . . . . . 62

6.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Chapter 7 Conclusions and Future Directions 65

Bibliography 68

Vita 75

ix

List of Figures

2.1 Multiphoton ionization . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Atomic potential, distorted potential and barrier suppression . . . . 9

2.3 ATI vs inverse bremsstrahlung . . . . . . . . . . . . . . . . . . . . . 13

2.4 Comparison of the total energy distribution with a Maxwellian . . . 19

2.5 Mechanism of fusion from exploding clusters . . . . . . . . . . . . . . 20

2.6 Illustration of the cluster target . . . . . . . . . . . . . . . . . . . . . 21

2.7 Fusion yield scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.8 Fusion contributed from the Maxwell tail . . . . . . . . . . . . . . . 25

2.9 Differential cross section for the 2H(d,3 He)n reaction . . . . . . . . 26

3.1 Overview of the THOR-laser . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Schematics of the target chamber . . . . . . . . . . . . . . . . . . . . 31

3.3 Gas-jet with supersonic nozzle . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Photo of target chamber . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1 Pressure scaling of Rayleigh scattering signals . . . . . . . . . . . . . 36

4.2 Temperature scaling of Rayleigh scattering signals . . . . . . . . . . 37

4.3 Time of flight histogram . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4 Pressure dependence of the fusion neutron yield . . . . . . . . . . . . 40

4.5 Energy dependence of the fusion neutron yield . . . . . . . . . . . . 41

x

4.6 Polarization dependence of the fusion neutron yield . . . . . . . . . . 43

4.7 Angular distribution of the neutron yield . . . . . . . . . . . . . . . 45

5.1 Schematics of the Z-machine at Sandia National Laboratories . . . . 48

5.2 Schematic illustration of a z-pinch driven hohlraum . . . . . . . . . . 49

5.3 Position of the detector . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.4 Schematics of the detector design . . . . . . . . . . . . . . . . . . . . 51

5.5 Schematics of the setup for the calibration . . . . . . . . . . . . . . . 53

5.6 Time of flight histogram for detector calibration . . . . . . . . . . . 54

5.7 Histogram of peak areas . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.8 Average pulse heights at different bias voltages . . . . . . . . . . . . 57

6.1 Schematics of magnetic mirror confinement . . . . . . . . . . . . . . 59

6.2 Illustrated circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.3 Schematics of laser triggered spark gap . . . . . . . . . . . . . . . . . 61

6.4 Test circuit for B-field formation . . . . . . . . . . . . . . . . . . . . 62

6.5 Simulation of the maximum B-field . . . . . . . . . . . . . . . . . . . 63

7.1 Schematic illustration of the setup for a rotating plasma filament . . 66

xi

Chapter 1

Introduction

The development of Chirped Pulse Amplification (CPA) [1] opened the way

for studies with ultra short, high intense laser pulses on table top lasers. Compact

laser systems providing peak powers of several terawatts are now available in many

laboratories where it is possible to generate focussed intensities of > 1018 W/cm2.

At such intensities the laser electric field becomes comparable to the electric field

felt by an electron in an atom. The physics of laser-matter interactions accessed a

new regime where atoms could be ionized almost instantaneously by intense laser

fields.

In particular the interaction of femtosecond lasers with atomic clusters now is

a field of high interest [2, 3, 4, 5], because it was observed that lasers very efficiently

couple into cluster gases [6] whereas the absorption in gases at near atmospheric

pressure is very ineffective. This is due to the different heating mechanisms in

both cases and will be explained later in this thesis. Clusters are accumulations of

≈ 103 − 105 atoms bound together by van-der-Waals forces. They form during the

expansion from a high pressure reservoir vacuum through a nozzle.

Atoms in clusters that are illuminated by an intense, ultra short laser pulse

1

get ionized. Electrons leave the cluster and the ionized cluster expands due to

Coulombic repulsion of the positive charged atoms. Depending on the ionization

time, which in turn depends on the intensity of the pulse and the pulse duration,

either the expansion of the partially stripped cluster or the full ionization is going

to happen faster. In the first case the cluster expands hydrodynamically whereas in

the latter case it Coulomb explodes [7]. For the Coulomb explosions the ions can

gain energies of many keV.

A fundamental fragment of the interest in laser-cluster interactions concerns

clusters of deuterium or lately also clusters formed from deuterated heteronuclear

molecules. Upon irradiation with a short, intense laser pulse, a gas of deuterium

clusters can exhibit extremely efficient deposition of energy creating a plasma with

energy densities reaching 105 J/cm3 [8]. The instantaneous ejection of almost all

electrons from the clusters results in a Coulomb explosion of the clusters in which

the ions gain sufficient energy to undergo dd-fusion [9, 10]. In 50 % of the fusion

events a characteristic 2.45 MeV neutron will be emitted:

D + D−→T (1.01MeV ) + p(3.02MeV )

D + D−→He3(0.82MeV ) + n(2.45MeV )

Both reactions have about the same probability. Hence the irradiated clusters act

as a reliable pulsed source for energetic, monochromatic neutrons.

Such a table-top neutron source utilizing pure deuterium clusters was first

presented by Ditmire et al. [4]. This method for producing fusion neutrons is very

attractive due to its high repetition rate, its inexpensive and compact design and its

easy handling. In addition, the neutron burst is ultra-short [11] and scales favorably

with increasing laser pulse energy [12].

2

Various other methods for neutron generation from laser-produced plasmas

have been demonstrated over the past few years [13]. Neutrons can be generated

in a secondary process where nuclear reactions occur in a sample material irradi-

ated by energetic electrons or radiation produced in the plasma. This process was

suggested as a possible basis for a neutron source by Schwoerer et al. who used

the radioactive decay of the sample as a means of measuring hard x-ray yields [14].

Using large scale laser systems, with focussed intensities exceeding 1019 W/cm2 it is

even possible to carry out nuclear physics experiments and to cause photoinduced

fission of 238U [15, 16].

The great interest for fast (MeV) neutrons relies on the various applications

especially in material science. In advantage to the high fluxes provided by accelera-

tors, plasma pinches or spallators that typically yield neutron pulses with durations

greater than a few nanoseconds [17], laser driven fusion plasmas can produce short

bursts of fast neutrons [11]. These short-pulse neutron sources open the possibility

of ultra fast (subpicosecond) studies for example of the material damage by neu-

trons [18, 19]. Such tests are particularly important for the construction of fusion

reactors. Other applications can be adopted in radiography [20].

Furthermore the use of facility-scale laser systems to achieve energy pro-

ducing fusion has been the goal of laser interaction experiments for many years

[21, 22, 23]. Neutron yields have been measured from both a gaseous deuterium

medium [24] and deuterated plastic targets [25].

The neutron yield of a cluster fusion source crucially depends the conditions

of the experiment like the cluster size, the laser intensity or the target density.

Cluster fusion sources are capable of yields up to 105 fusion neutrons per Joule of

incident laser energy using deuterium clusters [4]. Grillon et al. demonstrated that

3

even higher ion energies can be achieved from deuterated methane clusters [26].

This should lead to higher fusion yields due to an increased cross section [27, 28].

In this thesis we will present an experimental result for the dependance of

the neutron yield on the laser energy as well as on the angle of emission. This

investigation is aimed to characterize the physics of the plasma filament that emits

the neutrons.

As a first application of the fusion neutron source we employed it to cal-

ibrate a high sensitivity neutron detector [29] designed for operation on experi-

ments performed on the Z facility [30, 31] at Sandia National Laboratories. Typi-

cally, the detector will be used in single shot dd-pellet ignition [32] experiments in

which a relatively small neutron signal must be distinguished from a strong flux of

bremsstrahlung radiation.

The cluster fusion neutron source satisfies all the important demands for this

calibration. Monochromatic 2.45 MeV neutrons, which primarily will be observed

with this detector, are supplied at a high repetition rate and good statistics can be

achieved. The calibration profits from the low flux of bremsstrahlung emitted by

this source.

Furthermore femtosecond laser driven pulsed neutron sources are of particu-

lar interest for material studies, because they provide the opportunity to image the

neutron damage on a femtosecond time scale. But for material damage experiments

with neutrons much higher fluxes than provided by any known table-top laser driven

source are required. In this thesis we propose a method where the plasma filament

is confined by a magnetic mirror. This will counteract the expansion of the plasma

so that the ion density will not decrease that rapidly. For such a confinement fields

of about 200 Tesla are required. The magnetic field for the confinement will be

4

generated by miniature coils next to the plasma.

The purpose of this thesis is to characterize experimentally the cluster neu-

tron source and to propose a way to improve its yield for further applications. Also

a method for the calibration of a neutron detector is described.

The structure of this manuscript is as follows. In the next chapter we will

provide the theoretical background for the work that is issued in this thesis. This

includes a description of the ionization of clusters and the prevailing heating mech-

anisms. In chapter 3 the setup of the experiment for cluster fusion studies is de-

scribed. The presentation of results begins in chapter 4 with the characterization

of the cluster neutron source. In chapter 5 the calibration of a neutron detector for

use on Z at Sandia National Laboratories is described. A method for increasing the

neutron yield of the source is presented in chapter 6. This includes the description

of a electric circuit that generates a high magnetic field. Chapter 7 summarizes

the results of this work and discusses potential directions and applications for this

experiment.

5

Chapter 2

Laser Cluster Interactions

The purpose of this chapter is to introduce some of the basic concepts that

describe the interaction of intense, short laser pulses with atoms and clusters in a

gas. The following chapters will presume the background introduced here.

2.1 The Ponderomotive Potential

The oscillation of a strong laser electric field can drive an electron. The

equation of motion for an electron oscillating in free space in the absence of an

atomic ion can be written as

mex(t) = eE0 sinω0t (2.1)

where me is the electron mass, e is the electron charge, E0 is the peak electric field

and ω0 is the laser frequency. From the oscillating laser field the electron acquires

a kinetic energy of12mev(t)2 =

e2E20

2meω20

cos2 ω0t (2.2)

6

The cycle averaged kinetic energy of the electron is the quiver or ponderomotive

energy of the electron

Upond =12me〈v2〉 =

e2E20

4meω20

(2.3)

The ponderomotive energy at an intensity of 1016 W/cm2 for laser light with a

wavelength of λ = 1 µm is ≈ 1 keV .

2.2 Ionization Processes

2.2.1 Multiphoton Ionization

At high intensities photo-ionization can occur even if the photon energy

is below the ionization potential of the atom. An atom can gain sufficient energy

by absorbing more than one photon before the excited electron decays back to the

ground state. This process is called multiphoton ionization. Fig. 2.1 shows a

schematic picture of this mechanism.

Figure 2.1: Schematic of multiphoton ionization. An atom can be ionized by ab-sorbing more than one photon.

7

This picture is good until the laser strength becomes comparable to the

atomic field strength. This strong field begins with laser intensity of roughly ≥

1014 W/cm2. The actual ionization regime for a particular experiment can be de-

termined using the Keldysh parameter, which will be introduced later.

2.2.2 Tunnel Ionization

For higher intensities the laser electric field is strong enough to distort the

atomic potential (Fig. 2.2). At this point the effects on the Coulomb potential can

not be treated as perturbations anymore. A quasi-classical picture of an electron

trapped in the potential well of an atom gives a better agreement here. If the

distortion is strong enough, the electron can tunnel through the barrier, a process

called tunnel ionization.

A general relation for the tunneling rate of a complex atom has been worked

out by Ammosov, Delone and Krainov [33]. The so-called ADK-rate has been de-

rived by averaging the tunneling rate over a single optical cycle

Wtunnel = ωa(2l + 1)(l + |m|)!2|m||m|!(l + |m|)!

(2e

n∗)n∗IP×

(2E

π(2IP )3/2)1/2(

2(2IP )3/2

E)2n∗−|m|−1 exp[

2(2IP )3/2

3E]

(2.4)

where ωa is the atomic frequency, l and m are angular momentum quantum numbers,

n∗ is the effective principal quantum number, IP is the ionization potential of the

particular charge state and E is the laser electric field.

2.2.3 Barrier Suppression Ionization

As the laser intensity increases even further, the barrier gets suppressed below

the ionization potential of the atom. At this point the ionization rate becomes

significant. The effective potential seen by an electron in a Coulomb potential with

8

Figure 2.2: a) The electron wavepacket is bound by the Coulomb potential of theatom. b) For a laser distorted atomic potential the wavepacket has a probabilityto tunnel through the barrier. c) The barrier can be suppressed below the electronpotential for sufficient strong laser fields.

9

an external field E0 is

V (r) = − Ze2

4πε0r− eE0r (2.5)

By setting the first derivative equal to zero we get the radius for which the barrier

has its local maximum:∂V

∂r=

Ze2

4πε0r2− eE = 0

⇒ rmax =√

Ze

4πε0E0(2.6)

To calculate the required electric field which is sufficient to suppress the barrier, we

set the effective potential at r = rmax equal to the ionization potential of the atom:

E0 =I2P πε0Ze3

(2.7)

where IP is the ionization potential of the atom. The laser intensity is given as

I = cε02 |E0|2, where c is the speed of light. Therefore the corresponding intensity is

I0 =cI4

P π2ε302Z2e6

≈ 4 · 109 (IP [eV ])4

Z2[

W

cm2] (2.8)

From this equation the intensity for which the ionization rate becomes reasonable

can be estimated easily. Hydrogen (IP = 13.6 eV ), for example, will ionize at an

intensity of 1.4 · 1014 W/cm2. From this relation the appearance intensity of a

particular charge state by tunneling can be estimated. The results from this model

are in good agreement with the ADK tunnel ionization rate.

2.2.4 The Keldysh Parameter

A good criteria to determine which ionization process dominates during the

experiment is the Keldysh parameter. It is defined as

γ =

√IP

2Upond=

ω

ωtunnel(2.9)

10

where ω is the laser oscillation frequency and ωtunnel is the tunnel ionization fre-

quency. When the tunneling frequency exceeds the laser frequency, the tunnel ion-

ization will predominate. In the other case multiphoton ionization will be the dom-

inating mechanism.

For the work presented in this thesis we used laser intensities of about

1018 W/cm2, which corresponds to a Keldysh parameter of γ ≈ 0.01 for deuterium.

Hence we are certainly in the tunneling regime.

2.3 Plasma Heating

Several competing mechanisms are responsible for the coupling of laser

energy into a solid density plasma. Typically the energy is primarily transferred

to the electrons due to their lighter mass. By collisions or space charge effects the

electrons then accelerate the ions. Only heating mechanisms that are relevant for

gaseous, optically ionized plasmas illuminated by short laser pulses are considered

here.

2.3.1 Above Threshold Ionization (ATI)

Since we assumed that the primarily ionization process for the work we present

in this thesis is tunneling ionization, we can reduce the discussion of ATI to this

regime. ATI occurs, if an electron is ionized at a phase that is shifted by ∆ϕ > 0

from the peak of the laser electric field. The additional photon energy will than

increase the electron kinetic energy by

Ekin,ATI = 2Upond sin2 ∆ϕ (2.10)

For ∆ϕ = 0 the electron will not have gained any energy after the laser pulse has

passed, because the average acceleration will be zero. Since the probability of tunnel

11

ionization is highest at the peak of the E-field, we expect the majority of electrons

to ionize close to ∆ϕ = 0 for a linearly polarized field. The ATI energy will be small

compared to the ponderomotive potential. Therefore ATI is an ineffective coupling

of energy into a plasma.

2.3.2 Collisional Heating

Collisional heating is also known as inverse bremsstrahlung heating. An

electron that is accelerated by an incoming laser pulse will have the same energy

as before, once the electric field has returned to zero. This changes if the electron

undergoes collisions with ions while it is still accelerated. For example, if the electron

undergoes a 90 collision that occurs instantaneously, it loses all its velocity in the

direction of the e-field and maintains energy after the pulse has passed.

An estimation of the heating rate can be made assuming that the electrons

contribute their peak energy to the plasma upon every collision. The collision fre-

quency is

νei =dσ

dΩvnif(vth)dvth (2.11)

where dσdΩ is the differential coulomb velocity cross section, v is the electron veloc-

ity (given as the sum of the thermal velocity and the oscillatory velocity u(t) =

u0 sinωt), ni is the ion density and vth is the thermal velocity.

To obtain the heating rate we have to average over all possible scattering

angles and over a whole laser cycle. We get the cycle averaged energy deposited per

unit timedW

dt= ni2f(vth)dvth

Z2e4

me

1u0

lnΛ lnu0

vthfor u0 > vth (2.12)

where ln Λ is the coulomb logarithm. For u0 < vth the heating rate is zero. The

optimum collisional heating rate occurs if the oscillating velocity is comparable to

the thermal velocity. This means that the thermal velocity of the electrons gets

comparable to the ponderomotive energy of the pulse. To achieve this result we had

12

to assume that all collisions are elastic and that the collision time is small to one

cycle of the oscillation.

Figure 2.3: Schematic heating rate for ATI and inverse bremsstrahlung for Upond =1016 W/cm2. For small intensities ATI is the prevailing mechanism and for highintensities inverse bremsstrahlung dominates.

When a cluster plume is illuminated by an intense laser, field ionization

sets free initial electrons immediately, forming a high density plasma ball. Because

of the high electron ion scattering rate in this dense plasma, heating by inverse

bremsstrahlung dominates over ATI. As can be seen from Figure 2.3, this is much

more effective. Therefore laser absorption is significant enhanced for cluster gases

compared to atomic gases.

2.4 Cluster Formation

According to the ideal gas law, a gas that adiabatically expands from a high

pressure reservoir into vacuum cools down. The cooling causes the gas to condensate

13

and clusters form. This effect can be enhanced by directing the gas by a nozzle such

that the relative velocities of the particles in the gas get drastically reduced.

The efficiency of this process, and hence the size of the formed clusters,

depends on the backing pressure P0 in the reservoir, the initial temperature T0, the

geometry of the nozzle and the kind of gas used. The onset of cluster formation

as well as the size of clusters produced can be described by the empirical scaling

parameter referred to as the Hagena parameter [34]

Γ∗ = k(d/ tanα)0.85P0

T 2.290

(2.13)

where α is the expansion half angle, d is the orifice diameter of the nozzle and k

is a constant related to the inter-molecular bonding potential of the clustering gas

(e.g. k = 184 for hydrogen). Cluster formation is a statistical process. Usually

the distribution of cluster sizes is relatively broad. Gas jets with the same Γ∗

form clusters of about the same average size. For the regime of large clusters (>

103 atoms/cluster) the average number of atoms per cluster 〈NC〉 approximately

scales as

〈NC〉 ∼ Γ∗ 2.0 (2.14)

A convenient method of measuring the cluster size is optical Rayleigh scattering.

An interesting property of cluster media is, that they have the average density of a

gas whereas the single clusters have a near solid density.

2.5 Requirements and Simplifying Assumptions for

Plasma Treatment of Clusters

To describe the mechanisms of laser cluster interactions we treat the

illuminated clusters as a plasma. In the following we want to justify this model and

make some assumptions for the sake of simplicity.

14

A plasma treatment is only valid if quasi-neutrality is ensured for the am-

bit of the cluster. Hence the majority of ionized electrons have to be confined

to the cluster for the duration of the laser pulse. This is given for large clusters

(> 1000 atoms/cluster) where, like it is the case for a solid, the majority of elec-

trons are confined by the space charge.

Plasmas can shield out electric potentials that are applied to it. An electric

charge in a plasma attracts particles of the opposite charge that almost immediately

form a cloud around it. If there were no thermal motions (cold plasma), the isolation

would be perfect and no electric field would be present in the plasma outside the

clouds. For a finite temperature particles at the edge of the cloud can escape the

electric potential. The radius where the potential energy of these particles equals

their thermal energy is called the Debye-length [35]

λD =

√ε0kTe

ne2(2.15)

where k is the Boltzmann constant, Te is the electron temperature, n is the electron

density and e is the electron charge. A criterion for an ionized gas to be a plasma is

that it has to be dense enough such that the dimension of the cluster is much larger

than the Debye length. For typical parameters in our experiments the Debye length

is < 1 nm whereas the cluster diameters are in a range of 3 − 10 nm. Hence the

criterion is fulfilled.

The third requirement is that that the cluster has to hold together on the

time scale of the laser pulse in order to interact with it. Assuming sound speed an

expansion to 11000 of the initial density would take about 1 ps. Since the work was

done using femtosecond laser pulses this requirement is clearly satisfied.

To simplify the following calculations we assume the plasma to be spherical.

Furthermore it is assumed that all particles in a cluster experience the same laser

electric field strength. This is valid since the cluster diameter is much smaller than

15

the laser wavelength and the plasma skin depth. The ion density distribution is

assumed to be uniform across the cluster and the expansion is assumed to be self-

similar so that the electron density remains uniform throughout the expansion. An-

other assumption is that the temperature distribution across the plasma is isotropic.

2.6 Cluster Explosions

2.6.1 Cluster Expansion

The characteristic velocity for a plasma expansion is the plasma sound speed

cs =√

γZkTe

mi(2.16)

where mi is the ion mass and γ is the adiabatic index (γ = 35 for ideal gas). There

are two mechanisms that drive the cluster expansion. The repulsion between the

ions after a charge build-up on the cluster results in a Coulomb pressure

PCoulomb =Q2e2

8πr4(2.17)

where Qe is the charge build-up and r is the radius of the cluster. The thermal

motion of the hot electrons leads to a hydrodynamic pressure

PHydrodynamic = nekTe (2.18)

Notice that the scaling with the cluster radius is ∼ r−3 in the hydrodynamic

case (since ne ∼ vol−1) and ∼ r−4 in the Coulomb case. Hence the hydrodynamic

case gets more important for larger clusters. For the intermediate regime of those

two cases a calculation for the equation of motion of electrons in a uniform spherical

cluster was done by Breizman and Arefiev [36].

For this work only the regime of Coulomb explosions is of interest. Intensities

such as provided by the THOR-laser are sufficient to ionize D2 or CD4 clusters with

16

a diameter of a few nanometers within a few laser cycles. Hence the following

discussions will be restricted to this case.

2.6.2 Ion Energies

Like discussed earlier, electron-ion collision heat up the electrons efficiently.

But due to the extremely small disassembly time of the plasma filament [10], there

is insufficient time for the electrons to transfer their energy to the ions through

collisions. Instead the ions gain energy through Coulomb explosion.

The maximum energy for ionized clusters is given by the potential of the

outermost ions

Emax =〈q〉nie

2r2

3ε0(2.19)

where 〈q〉 is the average charge state in the cluster, ni is the initial ion density and

r is the cluster radius. The disassembly time is defined by the time required for a

uniformly charged sphere to grow to twice its initial radius [10] and for deuterium

clusters given by

tdis ≈ 0.8√

4πε0mD

nie2(2.20)

where mD is the mass of a deuteron. For a typical deuterium cluster density this time

is ≈ 20 fs. If the rise time from initial ionization intensity to an intensity sufficient

to remove the majority of electrons in the cluster is comparable to the disassembly

time, the cluster will explode while the charge density is maximum. For significantly

larger rise times or lower peak intensities, the cluster will start to expand before all

electrons are removed and the charge density will be reduced. Hence we need ultra

short laser pulses and high peak intensities to convert the maximum electrostatic

energy into ion kinetic energy.

The Coulomb explosion isotropically accelerates the deuterium ions to sub-

stantial energies, but only the surface ions acquire the maximum energy. The full

17

energy distribution is given by

f(E)dE = A√

EdE (2.21)

where A is a normalization constant and E > Emax. This distribution is shifted

towards high energies and the average energy is equal to 3/5 Emax. The peak

energies can be up to a few tens of keV . This is sufficient to give them a significant

probability for dd-fusion when colliding with ions from nearby clusters.

The ion energy distribution above is only valid for single cluster explosions.

Relying on previous studies [37] we assume a log-normal distribution for the cluster

sizes for our gas jet. The density for clusters of the size N can be written

nC(N) =nC,total

Nσ√

2πexp(

−(lnN − µ)2

2σ2) (2.22)

where µ and σ are the mean and standard deviation and N is the number of

molecules or atoms in a given cluster. The energy distribution for such an ensemble

of Coulomb exploding clusters is

f(E)dE ∼ g(e)√

EdE (2.23)

where g(E) is given by

g(e) =∫ ∞

NE

nC(N)dN (2.24)

and NE is a cluster size related to E.

The total energy distribution given by the convolution of the cluster size

distribution with the energy distribution for single clusters is almost Maxwellian as

can be seen from Figure 2.4.

18

Figure 2.4: Calculated total energy distribution. It is a good approximation toassume the ion energy distribution to be Maxwellian.

2.7 Neutron Yield Calculations

Deuterium ions from neighboring exploding clusters can have sufficient kinetic

energy to undergo fusion processes. The underlying principle of this mechanism is

illustrated in Figure 2.5.

For various application of the cluster source a high neutron yield is required.

Therefore we are interested in predicting the yield for various configurations. For

sake of simplicity we will only look at pure deuterium clusters. The beam target

consists of a hot plasma filament surrounded by a cold ion plume. If two deuterium

ions approach each other to a sufficiently small distance, fusion occurs. This is only

possible for high kinetic ion energies. The possible dd-fusion processes are described

by the reactions

D + D−→T (1.01MeV ) + p(3.02MeV )

19

Figure 2.5: Schematic illustration of the mechanism for nuclear fusion from explod-ing deuterium clusters. The laser irradiated clusters Coulomb explode and createplasmas with sufficient ion energies for substantial nuclear fusion.

D + D−→He3(0.82MeV ) + n(2.45MeV )

Both reactions have about the same probability, hence in every second fusion reac-

tion a neutron is produced. To calculate the yield we have to look at two different

regions for neutron production. The fusion processes can either happen from colli-

sions of two hot electrons in the filament or from collisions of hot ions that leave the

filament with cold ions in the plume. The total yield is the sum of both processes.

For the fusion yield inside the plasma filament an approximation is given by the

expression

Yfilament ≈τdis

2

∫n2

i 〈σv〉dV (2.25)

where τdis is the disassembly time of the plasma filament, 〈σv〉 is the velocity aver-

aged fusion cross section and V is the initial volume of the plasma. A factor of 12

20

Figure 2.6: Illustration of the cluster target. The laser hits the beam target 2−3 mmbelow the nozzle. Fusion neutrons can be produced in the plasma filament and inthe cold surrounding plume.

is included in this expression to account for the indistinguishability of the two ions

that collide. Moreover the plasma disassembly time τdis reflects that the fusion yield

from the filament also depends on the ion density. The contribution from reactions

in the plume is

Yplume ≈ Ni

∫〈σv〉dl (2.26)

where Ni is the number of ions leaving the filament and 〈σv〉 is the fusion cross

section for the plume. Whereas in the first case the cross section is weighed by the

ion velocities given by a Maxwellian distribution, the cross section for the plume

refers to an individual ion velocity v hitting a particle at rest. Since the probability

for fusion events is comparably low, the contribution from the plume is minor. For

this reason we limit the further discussion to fusion events in the hot filament.

21

For the temperature dependance of the fusion cross section 〈σv〉, an empirical

expression is given by [38]

〈σv〉DD [cm3

s] ≈ 2.33 · 10−14 T−2/3 [keV ]e−18.76 T−1/3 [keV ] (2.27)

which was verified by experimental data for temperatures below 25 keV . The plasma

disassembly time can be given by

τdis = γV 1/3

v(2.28)

where γ is a dimensionless geometrical factor, V is the volume of the plasma filament

and v is the average ion velocity given by

v =

√16Ei

3πmi(2.29)

We now assume, that the laser energy is completely absorbed in the plasma. Hence

the average ion energy Ei equals the laser energy divided by the initial number of

ions

Elaser = NEi = V niEi = V ni ·32kBT

V =Elaser

ni · 32kBT

(2.30)

Using equations (2.29) and (2.30) we can now rewrite the plasma disassembly time

in known quantities

τdis = γV 1/3

v=

γ( Elaser3/2kBTni

)1/3√16 · 3

2kbT/3πmi

= 0.547 ·γE

1/3laserm

1/2i

n1/3i (kBT )5/6

(2.31)

To solve the integral we make the assumption that not only the ion density, but also

the temperature and therefore the fusion cross section are constant over V . Using

(2.27) and (2.31) we find the fusion yield to be

Y ≈ 1.662 · 1026 γ · E4/3laser · m

1/2i · n

2/3i · 〈σv〉

(kBT )11/6(2.32)

22

As we can see from Figure 2.7 the fusion yield has a maximum at T = 15.6 keV .

Left of the maximum the yield rises due to the positive slope of the fusion cross

section. At the maximum the effects from a decreasing disassembly time starts to

dominate and the yield decreases.

Figure 2.7: Calculated fusion cross section a) and fusion yield scaling b) as a functionof ion energies. The fusion cross section grows steadily with higher ion energies. Thefusion yield scaling reaches its maximum at T = 15.6 keV (F. Buersgens [39]).

A typical ion density in a deuterium cluster plume is ni = 1019 cm−3 [4].

To make an upper bound calculation we assume the optimum average ion energy of

24.4 keV . Furthermore we use the value of the local maximum for the fusion cross

section. This gives us the upper bound of the fusion yield that only depends on the

23

laser energy and a geometric factor

Y ≈ 5.8 · 105 γ E4/3laser (2.33)

The fusion yield is twice the number of the neutron yield, because only every second

dd-fusion reaction releases a neutron. Compared with recent neutron yield measure-

ments [12] this result turns out to be slightly overstated.

2.8 Expected Angular Distribution

One of the observations we present in this thesis concerns the angular

distribution of the neutron yield. In this section we will go into the details of some

mechanisms happening in the beam target.

As we can see from Figure 2.8 most of the fusion events emanate from col-

lisions of ions in the high energy tail of the Maxwellian distribution. The steep

increase of the fusion cross section overcompensates the relative small number of

ions. R. Brown et al. [40] measured the differential cross section for the dd-fusion

reactions with high precision for ion energies > 20 keV . Since only about 3% of the

fusion events are caused by ions with lower energies than 20 keV , we can use their

results for calculating the differential cross section for the cluster fusion source.

Brown et. al studied the differential cross section for the center of mass

system (cm). To account for the motion of the center of mass system we have to

convert their result to the laboratory system (l)

σl(θl, φl) =(1 + γ2 + 2γ cos θ)3

2 · |1 + γ cos θ|σcm(θcm, φcm) (2.34)

where γ is a coefficient given by the ratio of the speed of the center of mass in the

laboratory system to the speed of the observed particle in the center of mass system.

24

Figure 2.8: Calculated fusion yield contribution of Maxwell distributed ions as afunction of ion energy. For an average ion energy of T = 12 keV more than 97 % ofthe fusion events result from ions with energies of 20 keV and more (F. Buersgens[39]).

Based on geometric considerations γ is found to be

γ =

√m1m3

m2m4

E

E + Q(2.35)

where Q is the energy released by the nuclear process and E is the energy initially

associated with the relative motion in the center of mass system. In Figure 2.9 the

differential cross section is shown for the fusion reaction that yields neutrons and

an initial ion energy of El = 20 keV .

From Figure 2.9 we see that the differential cross section is higher in forward

and in backward direction. This can be explained with the conservation of momen-

tum. The energy of the ion hitting a particle at rest is much bigger than the energy

of the released neutron. Therefore the neutron has to fly away essentially along

25

Figure 2.9: The green curve shows a fit of the differential cross for the collision ofa deuteron with an energy of 20 keV with a deuteron at rest for the center of masssystem experimentally observed by Brown et. al [40]. The red curve shows the samefit converted to the lab system (F. Buersgens [39]).

the axis of collision. The fact that the anisotropy increases for higher ion energies

substantiates this explanation.

With this background we are capable of making a prediction for the angular

distribution of neutrons. Almost all of the neutrons emerge from collisions of hot

ions in the plasma filament. The extension of the filament is much longer in the

direction of the laser axis then perpendicular to it. Hence the majority of collisions

will happen along the laser axis. In combination with the differential cross section

we therefore expect a distribution with a higher yield along the laser axis.

26

Chapter 3

Apparatus for Cluster

Experiments

3.1 The Laser System

All experiments presented in this thesis were performed on the THOR-laser

system. The Texas High-Intensity Optical Research facility is a multi terawatt

table-top laser system providing 40 fs pulses with energies of up to 0.6 J at a

wavelength of 800 nm. The repetition rate is 10 Hz. THOR is based on the

concept of chirped pulse amplification (CPA) [1]. This means that an ultra short

pulse gets stretched in time before being amplified and compressed again. CPA

is required to avoid dangerously high intensities during amplification. The desired

unfocussed intensity for a terawatt laser is > 1012W/cm2 which is high enough to

damage optics. Furthermore at such intensities the materials in the laser chain have

a nonlinear index of refraction. Hence self-focussing, for example of perturbations

on the beam, can cause damage in long amplifier rods. CPA successfully deals with

these problems by dramatically reducing the intensity of the pulse in the amplifier

chain.

27

Figure 3.1 shows the schematics of the THOR laser system. In the Ti:sapphire

oscillator a 20 fs, 6 nJ pulse is created by achieving a fixed phase relation for various

cavity modes with different wavelengths (mode-locking). This pulse with a center

wavelength of 800 nm has a relatively broad spectrum of ≈ 30 nm full-width at

half-maximum (FWHM).

By a diffraction grating the spectrum of the pulse gets dispersed and the

following optics are arranged such that for shorter wavelengths the optical path

becomes longer than for longer wavelengths. The pulse gets stretched in time and

the pulse coming out of this stretcher has a duration of 600 ps. Consequently the

intensity is reduced by a factor > 104 and can safely be amplified.

Figure 3.1: Overview of the THOR-Laser. In three amplification stages the beamgains a maximum energy of 1.2 J before being compressed to about 40 fs. Thespectrum for the stretched pulse, which normally is in the infrared, is sketched as avisible spectrum.

28

The pulse gets boosted in three different amplification stages. They all con-

tain Ti:sapphire crystal as amplifying medium. The main advantage of this material

is its broad tunability which is required for the wide spectra of chirped pulses. It

also provides a large gain cross section and good thermal diffusivity. On the other

hand the relatively low saturation level and the short upper state lifetime limit the

output energy and the repetition rate.

Coming from the stretcher the pulse is injected into a regenerative amplifier.

In this cavity it gets amplified to about 2 mJ by passing a Nd:YAG laser pumped

Ti:sapphire crystal. The gain that can be achieved in each stage is limited by the

saturation fluence of the crystal (0.8 J/cm2 for Ti:sapphire). In the regenerative

amplifier saturation is reached after about 30 passes and the pulse is switched out

by a high-speed pockels cell at that point. In order to obtain higher energies, the

aperture of the seed pulse now is increased from 2 mm to about 4 mm before it

reaches the next amplifying stage.

In the four-pass the beam is guided through a bow-tie shaped array of optics

that has a Ti:sapphire crystal in the middle. The pulse passes this crystal, which

is pumped by the same laser as the regenerative amplifier, four times. The energy

after the four-pass is > 20 mJ .

The final amplification happens in a five-pass amplifier. Two q-switched

1.4 J Nd:YAG lasers pump a 20 mm diameter Ti:sapphire crystal. By intentionally

mistiming the pump pulses with respect to the seed pulse, the output energy of the

five-pass can be varied over a range of 6 mJ − 1.2 J .

After amplification a vacuum spatial expands the beam to its final aperture

of 50 mm. In a single grating pulse compressor the pulse duration gets compressed

to 40 fs by reversing the effects from the stretcher. The optical path for smaller

wavelengths now is shorter and the geometry of the compressor is designed such that

the differences in pathlengths from the stretcher are exactly compensated. However

29

the initial pulse duration of 20 fs can not be achieved anymore. One reason for this

is that it is impossible to compensate all dispersion effects that the pulse experi-

ences in the various optics it passes during amplification. Therefore the pathlengths

through the whole assembly of stretcher, amplifier and compressor will always be

slightly different for different wavelength. In addition to this mechanism the spec-

trum narrows during amplification because the gain in the Ti:sapphire crystals is

lower for the edges of the spectrum, an effect that is called gain narrowing. Owing

to Heisenberg’s uncertainty principle a narrowed spectrum corresponds to a longer

pulse.

3.2 The Target Chamber

All experiments were performed in a vacuum chamber that is connected to the

compressor by a vacuum transport. The laser beam is guided from the compressor

to a switchyard, were it is redirected to this chamber. At this point the diameter of

the beam is 5.0 cm.

The geometry of the main elements in the chamber is shown in Figure 3.2.

The beam first hits a mirror that reflects it in an angle of 3.2 to a spherical mirror.

This f/10 optic focusses the beam under the nozzle of the gas jet. The focal spot

size can be assumed to be approximately 60 µm, which corresponds to an maximum

intensity of > 5 · 1017 W/cm2. This already accounts the losses in beam energy

of almost 50 % on the light pass from the final amplification stage to the target

chamber. Most of those losses occur during compression.

With a X-Y-Z stage the gas jet can be shifted in the optimum position for

each experiment. It is typically positioned in the center of the chamber. For polar-

ization experiments a λ/2 waveplate can be integrated into the beam pass. With a

clear aperture of 47 mm it reduces the beam energy by a small amount. The wave-

30

Figure 3.2: Schematic of the target chamber. The laser enters the chamber fromtop right. A spherical mirror focusses the beam under the gas jet.

plate can be rotated from outside of the vacuum to change the laser’s polarization.

3.3 Cluster Production

For cluster production a gas jet with a high backing pressure is used. Typically

the gas is compressed to≈ 1000 psi. The gas is cryogenically pre-cooled in a reservoir

in the gas jet. For this purpose nitrogen is guided through the coolant pipes that

surround the gas jet. For the case of deuterium clusters the gas has to be cooled

31

down to a temperature close to the condensation point of N2, for deuterated methane

clusters the temperature is typically close to the freezing point of water.

Figure 3.3: Schematics of the gas-jet with supersonic nozzle. (R. A. Smith et al.[41])

The opening of the gas jet is controlled by a trigger that operates a solenoid.

The applied magnetic force removes a poppet from the orifice of the nozzle. The

opening time can be varied. Typically it is ≈ 1 ms. Through a conical shaped

supersonic nozzle the gas then expands into vacuum.

3.4 Diagnostics

The quantitative measure of the neutron yield requires detectors that have a

time response of a few nanoseconds. Otherwise it would be impossible to distinguish

between the desired 2.45 MeV fusion neutrons, scattered neutrons, x-rays and cos-

mics. Also a high sensitivity is needed. The detectors have to be capable of tracing

32

single particles.

Neutron emission is observed by four scintillating neutron detectors. They

are composed of a cylindrical plastic scintillator with a diameter of 12.7 cm and 15.0

cm length and a photomultiplier tube (PMT) with 12.7 cm diameter, connected by

a conical Plexiglas light guide.

Figure 3.4: Photo of the target chamber. The picture shows a typical setup for anexperiment. Two detectors for energetic x-rays are positioned close to the chamberand a neutron detector is situated at an elevated position. The other detectors areto far away from the chamber to be seen here. The laser comes in from the rightside. The fusion reactions take place in the chamber in the center of the picture.

The plastic scintillator takes advantage of the fact that the cross section

for neutron-hydrogen interactions is comparatively large. Whereas neutrons easily

penetrate most other materials, their mean free path in hydrogen compounds is in

the order of a few centimeters. Neutrons can transfer significant amounts of their

33

energy to recoiling protons which subsequently excite atoms (and also some molecule

vibrations) in the medium. When decaying back to their ground state these atoms

emit so called scintillation light. It can be assumed, that for each 620 eV of depleted

proton energy one photon of 350− 500 nm wavelength is created in the scintillator

[42].

The material is highly transparent for the scintillation light. A reflective UV

coating reflects 80 % of the photons into the conical light guide that ends at the

PMT. Internal reflections between scintillator, light guide and PMT are avoided by

using an index matching oil for the connections. The PMT has a wide dynamic

range because the number of expected neutrons varies significantly, depending on

the neutron yield and the distance from the detector to the source. It has a gain

of ≈ 107 and an impedance of 50 Ω. The signals were recorded with a 5 GHz

Oscilloscope with a high bandwidth transient. A typical setup of diagnostics is

shown is Fig. 3.4.

34

Chapter 4

Characteristics of the Cluster

Neutron Source

In the following we will present results that characterize the cluster neutron

source in several ways.

4.1 Cluster Size Measurements

The maximum ion energies highly depend on the cluster size distribution

and so a good estimate of the average cluster size is important for interpreting

results. One method to do this is Rayleigh Scattering [43, 44]. We have chosen this

method, because it is non-destructive and the experiment is easy to perform. The

Rayleigh technique can be used for cluster sizes from 100 (the limit of scattering

light detection) to > 106 (the limit given by the scattering cross section) atoms per

cluster.

Optical scattering from a cluster jet typically occurs for a threshold of NC ≈

150 atoms per cluster [45, 44]. Measuring the pressure scaling of scattering after

this point allows us to estimate the average cluster size.

35

Figure 4.1: Measured pressure scaling of Rayleigh scattering signals for a) argon at293 K, b) xenon at 293 K, c) methane at 293 K and d) hydrogen at 80 K.

The scattering experiment was performed using a Nd:YAG laser providing a

532 nm long pulsed (a few ns) beam. The scattered light was collected by a lens

with a clear aperture of 50.8 mm at 90 from the incident laser and imaged to a

photo-multiplier tube. Background light was blinded out to a high degree.

For spherical clusters the scattering signal SRS is proportional to n0NC ,

where n0 is the density before clustering. We know that n0 is proportional to the

backing pressure P0 and hence find SRS ∝ P0NC .

The pressure scaling was measured for argon, xenon and methane at room

temperature and for hydrogen for a reservoir temperature of ≈ 80 K. The results

36

are shown in Figure 4.2. The observed pressure scalings for argon and xenon are in

general agreement with data reported in literature [41, 45, 46].

We estimated the cluster sizes for the pressures that are typically used in the

various experiments in our lab. For argon at 670 psi we found an average cluster

size of about 3.8 × 103 atoms per cluster corresponding to a diameter of ≈ 6.7 nm,

for xenon at 200 psi we estimated 5.1 × 103 atoms per cluster corresponding to a

diameter of ≈ 8.3 nm, for methane at 1000 psi we estimated 430 atoms per cluster

corresponding to a diameter of ≈ 4.2 nm and for cooled hydrogen at 1000 psi we

estimated 1.3 × 103 atoms per cluster corresponding to a diameter of ≈ 2.9 nm.

Figure 4.2: Measured temperature dependance of Rayleigh scattering signals formethane (left) and argon (right)

In addition to the pressure scaling we also observed the temperature depen-

dance of the average cluster size for methane and argon. The temperature scaling

depends on the Hagena parameter, the cluster size, the density and the Rayleigh

cross section. The scattering signal SRS is proportional to NC . For methane we

find SRS ∝ T−2.4 and for argon we find SRS ∝ T−4.7. Since for both gases optical

scattering can still be observed at room temperature, so that the onset of scattering

cannot be identified, we can not use this scaling to determine the cluster size.

37

4.2 Time of Flight Histograms

The detectors we used are not only sensitive to neutrons, but also to charged

particles and energetic rays like x-rays which are emitted from the plasma filament.

However most of those are shielded by the metal chamber walls. A method to

distinguish fusion neutrons, scattered neutrons, x-rays and cosmics is to record time

of flight (TOF) histograms. For every measurement such a histogram was plotted.

Figure 4.3: Time of flight histogram for a neutron detector in a distance of 4.37 mfrom the neutron source.

In Figure 4.3 one can clearly distinguish x-rays from fusion neutrons. The

data were taken by a detector positioned 4.37 m away from the neutron source.

Neutrons with an energy of 2.45 MeV travel with a velocity of 46.19 nsm and x-rays

38

propagate with the speed of light. For a distance of 4.37 m this corresponds to

a time of flight of 201.9 ns for neutrons and 14.6 ns for x-rays. This is in good

agreement with the two peaks in the time of flight data. We can see, that the source

is very clean and little x-ray emission comes along with the desired neutrons.

The neutron peak is followed by a tail of signals that are affected by scat-

tered neutrons. During the scattering process these neutrons lose energy and hence

velocity. In some of the histograms we found another small peak between the signals

from x-rays and neutrons. This peak might correspond to more energetic 14.4 MeV

neutrons with a velocity of 19.05 nsm . Those neutrons typically are created in a fusion

reaction of deuterium and tritium. Therefore it is possible that tritium generated

by the reaction D +D−→T (1.01MeV )+p(3.02MeV ) undergoes a secondary fusion

reaction yielding 14.4 MeV neutrons. Since the signals in the appropriate area were

small we need an increased neutron yield to confirm the existence of D+T fusion

processes in the plasma filament.

4.3 Pressure Dependance of the Neutron Yield

To find the optimum backing pressure for cluster fusion experiments, we

scanned the pressure dependence for a range of 400 − 1100 psi. The energy on

target was 320 mJ . Larger clusters lead to higher laser absorption [10]. According

to equation 2.19 the maximum kinetic energy of the deuterons increases with the

cluster radius. Hence a higher neutron yield is expected for larger clusters.

Figure 4.4 shows that the yield increases as pressure rises. After passing a

rollover point at ≈ 1000 psi, the yield decreases as the pressure increases. This

rollover can be explained by propagation effects in the low density wings of the

cluster plume. As the pressure rises the cluster diameters in the plume increase and

so does absorption. At the rollover point absorption by clusters in the outer regions

39

Figure 4.4: Measured pressure dependance of the neutron yield for an energy ontarget of 320 mJ .

of the plume depletes the laser energy before it penetrates into the high density

regions of the jet. For most of the following experiments we used a backing pressure

of ≈ 1000 psi to achieve a high yield.

4.4 Energy Dependance of the Neutron Yield

One great advantage of the cluster fusion neutron source is, that the neutron

yield scales favorably with increasing laser pulse energy [12]. We observed the energy

dependance of the neutron yield for deuterium clusters for energies of 28 − 350 mJ .

For this measurement we cooled the gas in the jet to about 80 K and used a backing

pressure of 1000 psi.

40

Figure 4.5: Measured energy dependance of the neutron yield for a backing pressureof 1000 psi and a gas jet temperature of 80 K.

From Figure 4.5 we can see that the fusion neutron yield increases with

higher laser energies. Using the least mean squares fit to a power law dependance,

the scaling was found to be ∝ E2.23 for low energies. This is consistent with previous

results [12]. However the scaling changes at ≈ 220 mJ to almost linear. This might

be due to a pre-pulse of the laser beam. At high energies such a pre-pulse can have

sufficient intensity to partially ionize the clusters. This would lead to an expansion

before the main pulse arrives. The average kinetic energy for ions and therefore the

fusion neutron yield from Coulomb explosions of pre-expanded clusters obviously is

smaller. The maximum yield observed in this experiment was 1.4 × 104 neutrons

per shot.

41

4.5 Polarization Scan

For the case of CD4 clusters we measured the polar distribution of the neutron

emission. The laser light provided by the THOR laser is linear polarized. Since it is

the laser electric field that accelerates the electrons, this might also have an impact

on the direction in which the ions get their kinetic energy. A preferred direction

for ion velocity might than result in a enhanced neutron yield along the axis of

polarization.

Using a λ/2 waveplate we were able to scan the polarization dependance over

the full range of 180. For the measurements we used a 40 fs, 50 mJ pulse. The gas

jet had a backing pressure of 1000 psi and was cooled down to 273 K. We measured

the neutron yield at seven different polarizations with two detectors in positions

shifted by 90 to each other. A third detector recorded the overall yield so that we

were able to subtract the fluctuations of the total yield. For each polarization 700

shots were taken. Subsequently the signals were averaged and the obtained average

peak height was interpreted as a measure for the neutron yield.

The data plotted in Figure 4.6 show no obvious dependance on the polariza-

tion of the incoming beam. From this we can conclude that the cluster expansion

is isotropic or at least independent of the polarization of the ionizing e-field. Fur-

thermore the ion kinetic energy is not enhanced significantly by the laser electric

field.

This measurement gives no information about the distribution of the neu-

tron yield in the polar plane for a fixed polarization of the incoming light. This

distribution might show an anisotropy due to the unsymmetrical shape of the clus-

ter plume. Such a measurement would yield information about the contribution of

fusion events in the cold plume to the total neutron yield. Regrettably we could not

perform this experiment because of the geometry of our target chamber.

42

Figure 4.6: Measured polarization dependence of the fusion neutron yield. (F.Bursgens et al., to be published)

4.6 Angular Distribution of the Neutron Yield

As discussed in chapter two the angular distribution of the neutron yield

is expected to have a small anisotropy. An azimuthal scan performed by Grillon

et al. [26] showed an anisotropy of the neutron yield for a source similar to the

one we occupied. As clustering gas they used deuterated methane. However their

results do not show the expected enhancement in forward and backward direction,

but an inordinate structure. They explain this pattern with the contribution of

fusion events in the cold plume to the total yield, which they suspect to be higher

than discussed in the model above.

Since these results were rather surprising, we performed a measurement of

the angular distribution to ascertain the results. We used a setup almost identical

to that employed by Grillon et al.. Deuterated methane clusters were produced with

a backing pressure of 1000 psi pre-cooled to approximately 275 K by the supersonic

43

nozzle. This corresponds to a cluster size of ≈ 4.5 nm. A 40 fs pulse with energies

of 40− 300 mJ irradiated the target.

Because of the chamber design (Fig. 3.4) variations in the attenuation of the

neutron flux owing to different amounts of material (e.g. by flanges or windows)

along the path of the neutrons are a major issue for an angular scan. Therefore the

detector was situated at an elevated position with respect to the gas jet looking down

at an angle of 30−45. As can be seen from Figure 3.2 for these locations the path of

the neutrons is similar for every angular position. The distance between the nozzle

and the center of the scintillator was 0.28 m. In order to account for fluctuations

in the overall yield two additional detectors remained at the same position during

the whole measurement as normalization. The number of shots taken for a single

azimuthal angle varies from 200 to 1800.

Figure 4.7 shows the results of the angular scan. Due to the elevated position

of the detector the generated data has a polar component in addition to the desired

azimuthal component. For Figure 4.7 this already was taken into account by pro-

jecting the data points onto the plane of the laser. The variation of the statistical

errors reflects the variation in the number of shots for each data point.

We can clearly see an anisotropy in the plot. Forward and backward direction

appear to be preferential directions of neutron emission. The observed anisotropy

reveals a difference of ≈ 40 % for the forward direction compared to a direction

perpendicular to the laser axis. However the observed pattern is not consistent with

the pattern observed by Grillon et al..

To compare the data with the theory we simulated the expected distribution

for an average ion temperature of 12 keV . The results are also given in Figure 4.7

represented by the red curve. The simulation is based on a model of cylindrically

shaped plasma which is surrounded by a spherical beam target. A random spacial

distribution of clusters and a Maxwellian distribution for the particle velocities were

44

Figure 4.7: Measured and simulated angular distribution of the neutron yield. Theblue squares show the experimental data. Differences in the lengths of the errorbars reflect the amount of shots taken for each position. The result of a simulationfor a filament with an average ion temperature of 12 keV is given by the red curve.(F. Bursgens et al., to be published)

assumed. The results were obtained by calculating the probability for fusion events

in every azimuthal direction. The simulation shows the expected increased yield

along the laser axis. Compared to the backward direction the neutron emission in

forward direction is slightly augmented due to the geometry of the beam target.

4.7 Conclusions

In this chapter we have presented a series of measurements that characterize the

cluster fusion neutron source. We have shown a method to distinguish 2.45 MeV

45

fusion neutrons from other energetic radiation like x-rays, scattered neutrons or

cosmic radiation. We have estimated the average cluster sizes produced by the gas

jet for argon, xenon, methane and hydrogen. For typical pressures and temperatures

we found cluster sizes of 3 − 10 nm. The ideal cluster diameter for deuterium cluster

fusion experiments was found to be roughly 1000 psi. Furthermore we observed

on what parameters the neutron yields depend. We found that the neutron yield

scales favorably with laser energy. For low energy the yield is well characterized

by the power law dependence on pulse energy Y ∝ E2.23. The neutron yield seems

to be isotropic in polar direction, but we observed an anisotropy for the azimuthal

direction. This anisotropy is qualitative consistent with a simulation of the processes

in the plasma filament.

46

Chapter 5

Calibration of a Neutron

Detector

In this chapter we present a novel method of calibrating a neutron detector

designed for single shot operation. The detector was designed for operation on ex-

periments performed on the Z facility [30, 31] at Sandia National Laboratories. The

detector will observe the fusion yield on the Z-machine [47].

5.1 The Sandia Z Accelerator

The ultimate goal of the experiments performed on Z is to produce electric

power via inertial fusion confinement (ICF) [21]. ICF requires that small spherical

shells filled with deuterium (and often also tritium) get evenly compressed to a very

high density. At Z this is achieved by a z-pinch driven hohlraum.

Two z-pinches are created by a nested wire array, which consists of two con-

centric wire arrays. Each array is composed of 100-400 wires of 1−2 cm length with

a thickness of less than 10 µm [48]. A schematic picture of the geometry is shown

47

Figure 5.1: Schematics of the Z-machine at Sandia National Laboratories. Theelectric energy stored in 36 Marx generators (red) discharge through pulse forminglines (blue) into the wire arrays in the center. (R. B. Spielman et al. [31])

in Figure 5.2. The discharge of electric energy through the wires creates a magnetic

field. Lorentz forces than compress the exploded wire array with a extremely high

velocity. At the magnetic axis the vaporized particles collide with each other. The

kinetic energies of the particles are high enough to produce significant radiation. By

this radiation the surrounding walls of the hohlraum are heated. Subsequently the

walls emit x-rays that drive the ICF capsule. The advantage of this method is that

the indirectly driven capsule gets compressed with a high symmetry because of the

uniform illumination of its surface.

To achieve a substantial compression of the pellet the x-ray power has to be

enormous (i.g. > 100 TW [31]). To reach this a total electric energy of 11.4 MJ

is stored in 36 Marx generators providing a current of up to 20 MA through the

wire arrays. Highly synchronized laser-triggered switches allow the stored energy to

be discharged simultaneously. The wires in the arrays are made of Tungsten which

has the highest strength to weight ratio of all materials. Tungsten plasmas are very

efficient radiators at the pinch temperatures and the plasma densities found on Z.

The heating and vaporizing of these wires is initiated by a current pre-pulse with a

48

Figure 5.2: A schematic illustration of the double z-pinch driven hohlraum. Twowire arrays form a plasma that isotropically heats the hohlraum in between. Thefusion pellet is situated in the center of the hohlraum. Through the hole in the casethe pellet can be illuminated by the Z-beamlet for imaging the compression.

peak current of ≈ 300 kA. The main current pulse completes the vaporization and

ionization process. As a result of the huge currents powerful magnetic fields arise

that pinch the plasma on a vertical axis. The radiation from collisions of particles

in the plasma heats the hohlraum walls to ≈ 150 eV . For the x-ray radiation emit-

ted from the walls a power of 290 TW have been observed [48]. This results in a

compression of the pellet to about half its initial radius.

49

5.2 The Neutron Detector on Z

One of the principal diagnostics in large scale inertial confinement fusion exper-

iments is a measurement of the absolute fusion neutron yield. For this reason a high

sensitivity neutron detector was designed [29]. This detector will be used in single

shot dd-pellet ignition experiments [32] in which a relatively small fusion neutron

signal must be distinguished from a strong flux of bremsstrahlung radiation. With

this in mind, the detector has been constructed with a unique shielding geometry.

Figure 5.3: Schematic illustration of positioning of the neutron detector on Z. Thedetector will be situated in the shielding case on the right. (L. E. Ruggles et al.,[29])

In Figure 5.3 the location of the detector on the Z experiment is shown. The

detector is positioned close to the target chamber. Its shield and support structure

rest on the Z transmission lines inside the Z vacuum vessel.

The detector consists of a scintillator and a microchannel plate photomulti-

plier tube (MCPPMT). A prism coupled with index matching grease reflects light

from the scintillator onto the photocathode of the MCPPMT. With a thickness of

50

75 mm the scintillator (Saint Gobain type BC420) matches the dd-neutron mean

free path of 75 mm. Its 100 mm × 25 mm front surface area is located 90 cm

from the ICF capsule. The scintillator is coated with TiO2. Along with the power

supply and a diode laser alignment system the whole array is sealed in an air-filled

aluminum housing. The detector geometry is shown in Figure 5.4.

Figure 5.4: Schematics of the detector design. The upper picture shows the shieldinggeometry and the lower picture sketches the detector design.

The MCPPMT (Burle 85104-501) has a response time of 2 nanoseconds.

Combined with the neutron transit time and the 1.3 nanosecond response of the

scintillator it produces a 3 to 5 nanosecond single neutron response [29]. The effects

of this fast system response are ability to differentiate between prompt neutron

signals from scattered neutrons and a high signal to noise ratio.

Z produces abounding amounts of high photon energy x-rays. Since both

51

the scintillator and the MCPPMT are sensitive to x-rays the detector requires a

shielding against bremsstrahlung. The scintillator response to high energy x-ray

photons and 2.45 MeV fusion neutrons is roughly the same, but the number of

high energy x-rays is about eight orders of magnitude greater than the expected

number of neutrons. Hence the shielding has to fulfill very special requirements. Up

to 54 cm of steel and 31 cm of tungsten are situated between the scintillator and

the capsule area. The geometry of the double z-pinch (Fig. 5.2) allows an almost

unimpaired neutron flight pass and severely attenuation of x-rays at the same time.

Furthermore the MCPPMT is placed to one side of the scintillator to avoid exposure

to x-rays from the pinch area. The shielding geometry is shown in Figure ??. It

provides adequate attenuation of x-rays up to ≈ 4 MeV .

5.3 Calibration Data

The Z accelerator at Sandia National Laboratories is a single shot machine.

This limited repetition rate requires the use of a neutron detector which is well

calibrated to measure the absolute yield on a single shot.

The calibration was performed by driving the cluster fusion source the laser

system providing 40 fs pulses at a wavelength of 800 nm and a repetition rate of

10 Hz. The laser pulse with energy of 0.1 − 0.5 J was focused into a dense plume

of deuterium clusters by an f/10 spherical mirror to an intensity of ≈ 1017 W/cm2.

Clusters were generated using a gas jet consisting of a 24 mm long conical noz-

zle with an opening angle of 10 and an orifice of d = 750 µm. The deuterium

gas reservoir backing the jet was cryogenically pre-cooled to ≈ 100 K with liquid

nitrogen and expanded from a pressure of 70 bar into vacuum to form clusters of

radius approximately 3−10 nm (with a rather broad size distribution). The clusters

were irradiated approximately 2−3 mm under the nozzle where the average atomic

52

density was ≈ 1019 cm−3. In principle, neutrons can be produced at the 10 Hz

repetition rate of the laser. However, in this experiment, the gas jet was operated

once every six seconds because of the limited pumping capability of the vacuum

system.

Figure 5.5: Schematics of the setup for the calibration. The calibrated detector ismarked with a ”D”.

The neutron detector is operated far below its saturation level, and hence

the signal produced in the scintillator is proportional to the total neutron yield.

The bias voltages of the photomultiplier tube were varied from 2800 V to 3500 V to

observe the effects on the signal. During the calibration the detector was positioned

at a distance of 2.0 m from the laser focal spot. This distance assured that, with

an appropriately lowered fusion yield, neutrons were observed in single particle

detection mode with roughly one neutron observed every 10 shots. The signal was

recorded with a 5 GHz oscilloscope and the small initial x-ray pulse was easily

distinguished from the much larger neutron pulse which arrived ≈ 100 ns later.

The total neutron yield was also monitored with four additional neutron detectors

53

placed at distances of 0.40 m, 2.21 m, 2.40 m and 6.10 m. The schematic of the

calibration is illustrated in Figure 5.5.

To discern the dd-neutrons we plotted a time of flight histogram of the mea-

sured data. A representative TOF spectrum from the Z neutron detector is illus-

trated in Figure 5.6. This shows the separation between x-rays and fusion neutrons.

The zero time point was determined from the arrival of the initial x-ray pulse. We

identify the peak in the histogram at 92.8± 3.7 ns as the 2.45 MeV neutrons from

the dd-fusion reaction. This time of arrival is consistent with the expected time of

flight of 92.38ns for a 2.00 m distance. The low-energy tail of the neutron peak is

due to scattered neutrons from the surrounding walls of the lab. The small peaks

before 20 ns are caused by ballistic x-rays from the plasma and scattered x-rays

from the chamber walls.

Figure 5.6: Measured time of flight data. All signals over the noise level of 0.55 mVare plotted in this diagram. The included graph shows a typical signal of a singleshot.

54

A typical operating voltage for the detector will be a MCPPMT bias voltage

of 2800 V . We recorded 7000 shots at this setting. A discrimination threshold was

set at 0.55 mV and only peaks above this limit were taken into account. We assumed

that signals occurring in a time window of 22 ns were generated by unscattered

neutrons. Using this condition, a total number of 643 shots showed fusion neutrons

with energy of 2.45 MeV .

The number of neutrons produced in the deuterium plasma was regulated

by varying the laser pulse energy so that less than every tenth laser pulse resulted

in a signal on the detector. Previous experiments have shown that the fusion yield

in these deuterium cluster plasmas varies roughly as the square of the laser energy

[12]. With a laser energy of ≈ 0.2 J the total neutron yield was about 2 × 103

neutrons per shot, confirmed by the detector furthest away from the target assuming

an isotropic neutron distribution. This yielded a suitable neutron flux level for the

calibration. At a 2.0 m distance from the fusion plasma this corresponds to < 700

neutrons during 7000 shots on an area equal to the detectors scintillator surface

area assuming an isotropic neutron distribution. This is in good agreement with the

number of signals recorded.

For every fusion neutron signal above the threshold value and within the

22 ns TOF window, the peak areas were calculated. The signals were integrated for

a time window of 60 ns to reduce the errors arising from ringing in the acquisition

circuit. None of the signals showed a second peak from scattered neutrons or other

rays during this time interval. Figure 5.7 shows the histogram of peak areas. Its

shape results from the distribution of energy that the neutrons transfer to the scin-

tillating material. The average peak area was found to be 22.08 ± 0.87 mV ns. It

is expected, that the detector will interact with 245± 16 neutrons [29] on Z leading

to a statistical uncertainty of 8 %.

With higher MCPPMT voltages the peak areas increase exponentially. Though

55

Figure 5.7: Measured histogram of peak areas. 643 signals during 7000 shots wereassumed to be caused by unscattered neutrons. The histogram of peak areas givesinformation about the average signal form.

the statistics in this analysis were not as good as above, the measured sensitivity on

this voltage agreed with the normalized single photoelectron MCPPMT gain stated

by the manufacturer. Figure 5.8 shows the average peak height as a function of

MCPPMT voltage. The average pulse height appears to vary linearly with bias

voltage.

5.4 Conclusions

We have presented a novel method to calibrate neutron detectors designed

to measure total fusion neutron yield from single shot fusion experiments. We used

56

Figure 5.8: Measured average pulse heights at different bias voltages.

2.45 MeV neutrons from the plasma created by laser irradiated deuterium clusters.

We find that this cluster fusion source is an ideal neutron source for this application,

as it is very monochromatic, is largely clean from x-rays and drives from a point

like pulsed source with well defined flight time to the detector. The source provided

neutrons at a high enough repetition rate to achieve statistics that limit the error for

measurements using the detector almost completely to the statistical uncertainties

of the total yield.

57

Chapter 6

Pulsed Magnetic Mirror

Confinement of the Plasma

Filament

Before the cluster neutron source can be used for material science and some

other applications, the neutron yield has to be increased by some orders of mag-

nitude. The further progress on laser systems will definitely help to increase the

neutron production, but the required number of neutrons can only be reached by

other improvements.

6.1 Confinement of the Plasma Filament

From equation 2.26 we can see that a longer disassembly time of the plasma

will result in a higher yield. One possibility to achieve this is to apply a magnetic

confinement device to the cigar shaped plasma filament. The possibility of combining

a hot, laser produced plasma with a magnetic confinement device was first discussed

58

by Mayer, Berk and Forslund [49]. Since the disassembly time of the plasma is

< 100 ps a significant enhancement of the neutron yield could be achieved even for

confinement times in the order of a few nanoseconds.

The plasma expands predominantly in radial direction. We want to confine

the plasma at densities close to the initial density of 1019 cm−3. The point where

the plasma pressure equals the magnetic field pressure can be found with the plasma

parameter β which is given by

β =2µ0nkT

B2(6.1)

Stagnation of the plasma is achieved at the point where β = 1. For ion densities

between 1018 cm−3 and 1019 cm−3 and a temperature of 5 − 10 keV this requires

peak B-fields around 200 T .

Furthermore the Larmor radii should be less than the plasma size to achieve

confinement in the radial direction. The initial diameter of the plasma filament is

about 100 µm. To force 10 keV deuterons on an equivalent gyro radius B-fields of

more than 150 T are needed.

Figure 6.1: Schematic of magnetic mirror confinement

59

The confinement time of the plasma is limited not only by the pulse duration

of the magnetic field, but also by the particle losses through cross field diffusion of

the plasma in radial direction and through the loss cone of the magnetic mirror.

It turns out that for the desired two loop configuration the cone losses give the

dominant time scale

τcone = 0.78τii ln√

Bmax

Bmin− 1 (6.2)

This longitudinal escape time depends on the ion-ion collision time τii and the ratio

of the maximum magnetic field Bmax to the minimum magnetic field Bmin. For

ion densities of ≈ 1019 cm−3 the plasma confinement time is ≈ 100 ns. Hence a

magnetic field of more 200 T for ≈ 100 ns should be able to increase the fusion yield

by a factor of 1000 over previously observed yields in this experiment.

Figure 6.2: Schematic illustration of the circuit design for pulsed magnetic confine-ment.

60

Figure 6.3: Schematics of laser triggered spark gap. The gap between the electrodesis closed by a laser induced plasma.

6.2 Creating a High Magnetic Field

As we have discussed above for a reasonable confinement time the peak

magnetic fields required for substantial yield enhancement have to be > 200 T . Our

approach to this problem uses a small, pulsed magnetic magnetic mirror configura-

tion consisting of two coils.

61

6.2.1 Design of the Circuit

The main idea if the circuit that will provide the magnetic field in our experiment

is that a capacitor discharges through a low inductance, low resistance circuit which

contains the magnetic mirror coils. The concept of the circuit is illustrated in Figure

6.2. Currents as high as a few tens of kA are needed to create a magnetic field of the

desired strength with coils that fit to the dimensions predefined by the dimensions of

the cluster fusion neutron source. Therefore the capacitor used for the experiment

has to be capable of storing electric energy at voltages > 150 kV . The capacitor is

charged with a high voltage supply, e.g. a pulsed Marx generator.

Figure 6.4: Schematics of the circuit for testing B-field characteristics.

We expect the discharge pulse not to be much longer than 100 ns at a

sufficient current to create a B-field of 200 T . The peak rise time will be even shorter.

To guarantee cooccurrence of the laser driven plasma and the peak magnetic field the

discharge process has to be triggered with response times of a few nanoseconds. For

this reason we integrated a femtosecond laser triggered spark gap into the circuit.

The trigger pulse will be driven by a small fraction of the main pulse that is split

from the main pulse before compression.

The laser triggered spark gap can be filled with nitrogen. We designed it to

62

be adjustable in breakdown voltage by varying the pressure of the nitrogen up to

60 psi. The breakdown voltage in air was found to be 29 kV .

6.2.2 Results

The prove our concept of magnetic field generation suitable for micro plasma

confinement we built a scaled down test circuit to study its characteristics. A DC

power supply charges a capacitor with a capacitance of 0.1 µF to 40 kV . The

pressure in the spark gap is 30 psi which assures the breakdown voltage to be much

higher than 40 kV .

For two coils with 6 turns each, a radius of 2.7 mm and a separation of 4 mm

we simulated the temporal behavior of the magnetic field. From Figure 7.1 we can

see that the circuit is a overdamped system. The maximum B-field has a peak at

13 T which is still more than an order of magnitude below the desired 200 T .

Figure 6.5: Simulation of the maximum B-field for a 40 kV discharge from a 0.1 µFcapacitor. The calculations were done for a total inductance of 140 nH and a totalresistance of 3.1 Ω.

Regrettably no data for the test circuit magnetic field could be taken so far.

63

6.3 Conclusions

We have presented a method of enhancing the neutron yield for a laser driven

source using magnetic mirror confinement. A capacitor discharge through two small

coils was calculated to be capable of producing magnetic fields up to 200 T for

more than 100 ns. With these magnetic fields we expect to be able to increase the

confinement time of the plasma filament, which goes almost linear with the neutron

yield, by a factor of 103. However the method could not be verified in experiments

so far.

64

Chapter 7

Conclusions and Future

Directions

The purpose of this work has been to characterize, apply and improve a laser

driven fusion neutron source that relies on the efficiency of laser-cluster interactions.

The motivation for the studies presented in this thesis was to get one step closer to

a laser driven neutron source for femtosecond time resolved material studies and to

get a better understanding of the mechanisms happening in the plasma filament.

For this reason different properties of the source were experimentally inves-

tigated. We have found the average cluster sizes to be typically in the range of

3 − 10 nm for the gas jet used. The optimum size for experiments with deuterium

clusters was found to be ≈ 3 nm. We have shown that the neutron yield scaled

favorably with laser energy.

The neutron yield was found to be independent of the laser polarization, but

an anisotropy was observed for the azimuthal plane. The neutron rate varied by

as much as 40 % between the laser axis and an angle perpendicular to it. This

measurement is qualitatively consistent with a simulation of a plasma in a cold

plume.

65

As a first application for the source we have presented a novel technique to

calibrate neutron detectors designed to measure total fusion neutron yields from

single shot fusion experiments. Because of being very monochromatic, largely clean

of x-rays and point like with a well defined flight time to the detector, we found the

cluster fusion neutron source to be ideal for this application.

Finally we have described a method of improving the neutron yield using

magnetic mirror confinement. We have derived that the yield should be increased

by a factor of 103 for a confinement of 100 ns. We have shown that this could be

achieved with a magnetic field of about 200 T generated through a discharge circuit.

Figure 7.1: Schematic illustration of the setup for a rotating plasma filament. Thecurrent induced to the plasma forces the plasma to rotate due to E × B forces.

As we have described in chapter 6, a magnetic mirror confinement experiment

66

is promising for improving the neutron yield by a few orders of magnitude. However

for the realization of this idea a lot of work has to be done. Different coil designs

have to be simulated and tested to guarantee an optimum field generation. Also

problems concerning the application of very high voltage have to be solved.

Once working, the magnetic mirror confinement might not only help to in-

crease the fusion neutron yield, but also open possibilities for new exciting exper-

iments. For example applying a radial electric field to the plasma filament should

lead to rotation of the plasma [50]. This is very interesting because many astrophys-

ical phenomena include rotating plasmas. Furthermore for high rotation velocities

and under certain conditions self confining Magneto-Bernoulli states might form

[51]. This would help to explain phenomena like plasma jets from supernovae.

67

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Vita

Rene Hartke was born in Lohne (Oldb./Germany) on October 17th in 1979, the son

of Clemens Hartke and Hedwig Hartke. He graduated with the Abitur at Gymna-

sium Lohne in 1999. One year later he entered the Universitat Wurzburg where he

received the Vordiplom in 2002. In August 2003 he entered The Graduate School

at The University of Texas.

Permanent Address: Rene Hartke

Am Grevingsberg 25

49393 Lohne (Germany)

e-mail: R.Hartke@gmx.de

This thesis was typeset with LATEX2ε1 by the author.

1LATEX2ε is an extension of LATEX. LATEX is a collection of macros for TEX. TEX is a trademarkof the American Mathematical Society. The macros used in formatting this thesis were written byDinesh Das, Department of Computer Sciences, The University of Texas at Austin, and extendedby Bert Kay and James A. Bednar.

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