RICE UNIVERSITY

NOVEL PERMANENT-MAGNET PENNING TRAP

FOR STUDIES OF DIPOLE-BOUND NEGATIVE IONS

by

Leonard Suess

MASTER OF SCIENCE

HOUSTON, TEXAS

DECEMBER, 2001

RICE UNIVERSITY

Novel Permanent-Magnet Penning Trap

for Studies of Dipole-Bound Negative Ions

by

Leonard Suess

A THESIS SUBMITTED

IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE

Master of Science

APPROVED, THESIS COMMITTEE:

F.B. Dunning, ChairProfessor of Physics

G.K. Walters, Sam and Helen WordenProfessor of Physics, Emeritus

P. PadleyAssistant Professor of Physics

HOUSTON, TEXAS

DECEMBER, 2001

ABSTRACT

Novel Permanent-Magnet Penning Trap

for Studies of Dipole-Bound Negative Ions

by

Leonard Suess

Low-energy electron transfer between a Rydberg atom and a target molecule can

result in formation of long-lived metastable negative ions. Here we describe a novel permanent-

magnet Penning trap designed to examine the lifetime of such long lived metastable negative

ions. With the help of ion trajectory calculations, the characteristics of the trap have

been investigated and the most eective methods for ion injection have been established.

Collisions with SF6, which has a high electron attachment rate, result in the formation

of SF6 ions which are known to have a long intermediate lifetime. Comparisons between

experimental SF6 trapping data and ion trajectory calculations are discussed that demonstrate

the capabilities of the trap. Future experimental studies are also proposed.

Acknowledgments

A big thank you to Dr. Barry Dunning for his guidance and insight. Priya, thanks

for sharing your knowledge with me and for being such a wonderful friend. I am grateful to

Shannon Hill whose tireless eorts allowed a detailed investigation of the trap used in this

work. I have also beneted greatly from the interactions of all the other graduate students

and post docs in the laboratory. Their advice and contributions are greatly appreciated.

I would like to thank my family for their love and support. I am grateful to my

parents, who have constantly pushed me to better myself.

Most importantly, my deepest thanks go to my wife, Jessica. Her constant support

and love continues to push me forward.

Table of Contents

Abstract iii

Acknowledgments iv

List of Figures vii

1 Introduction 11.1 Electron Attachment Processes . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Rydberg Atom Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Ion Kinematics in an Ideal Penning Trap 42.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Equations of Motion for an Ion in an Ideal Penning Trap . . . . . . . . . . 5

2.2.1 Radial Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Axial Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Trapping Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Cylindrical vs. Ideal Penning Trap . . . . . . . . . . . . . . . . . . . . . . . 8

3 Experimental Apparatus 113.1 Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Potassium Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Permanent-Magnet Cylindrical Penning Trap . . . . . . . . . . . . . . . . . 16

3.4.1 Cladding Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.2 Trap Electrode and Electronics . . . . . . . . . . . . . . . . . . . . . 24

4 Simulating Ion Trajectories SIMION 284.1 Experimental Model in SIMION . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Loop Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Electric Potential Distributions for Trap Electrodes . . . . . . . . . . . . . . 304.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Experimental and Analytical Techniques 335.1 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 SF6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6 Conclusion and Future Work 406.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

v

References 42

A SIMION Code for Simulations 44

B Important Trap Dimensions and Characteristics 48B.1 Trap Dimensions and Quantities . . . . . . . . . . . . . . . . . . . . . . . . 48

vi

List of Figures

2.1 Ideal Penning trap with hyperbolic electrodes. . . . . . . . . . . . . . . . . 4

2.2 Magnetron motion superimposed on the cyclotron motion. . . . . . . . . . 5

2.3 Graph of expansion coecients D2 and D4 as functions of r0z0 . . . . . . . . 10

3.1 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Comparison of dierent magnetic materials. . . . . . . . . . . . . . . . . . 17

3.3 Magnetic Ohms analog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Cladding magnet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.5 Cross-sectional view of clad magnet. . . . . . . . . . . . . . . . . . . . . . . 21

3.6 Comparison of unclad and clad magnetic structures. . . . . . . . . . . . . . 22

3.7 Magnetization of the magnet assembly. . . . . . . . . . . . . . . . . . . . . 23

3.8 Axial magnetic eld within the magnet. . . . . . . . . . . . . . . . . . . . . 25

3.9 Cross-section of trap electrode. . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.10 Schematic of switching circuit. . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 SIMION model of experimental setup. . . . . . . . . . . . . . . . . . . . . . 28

4.2 Potentials on trap electrodes for various modes . . . . . . . . . . . . . . . . 31

4.3 Extraction of axial frequency for SF6 . . . . . . . . . . . . . . . . . . . . . 32

5.1 Pulse sequence for the bottom grid of the interaction region. . . . . . . . . . 34

5.2 TOF for 300s trapped SF6 ions. . . . . . . . . . . . . . . . . . . . . . . . 36

5.3 Arrival time spectrum for trapping times 185,300, and 416s. . . . . . . . . 37

5.4 Arrival time spectrum for a trapping time of 358s. . . . . . . . . . . . . . 38

5.5 Stability of SF6 in Penning trap. . . . . . . . . . . . . . . . . . . . . . . . 39

A.1 Electrode numbers for SIMION . . . . . . . . . . . . . . . . . . . . . . . . . 47

vii

Chapter 1

Introduction

1.1 Electron Attachment Processes

The study of electron-molecule interactions has grown signicantly over the past sev-

eral years due to their importance in biological, chemical, and physical systems [1, 2]. For

example, electron attachment is important in atmospheric studies involving pollutants such

as polycyclic aromatic hydrocarbons and multiply halogenated methane and ethane com-

pounds. Studies of their interaction with free electrons provide rate constant data used for

modeling their behavior in the atmosphere [3, 4].

Electron attachment to molecules can lead to reactions of the form,

e +ABC ABC ABC + e, (1.1.1)

e +ABC ABC AB + C, (1.1.2)

e +ABC ABC ABC. (1.1.3)

In reaction 1.1.1, the transient negative ion formed reverts back into a neutral molecule and

an electron (autodetachment). In reaction 1.1.2, the intermediate dissociates producing

a neutral and a charged fragment. In reaction 1.1.3, the intermediate is stabilized by

intramolecular vibrational relaxation leading to formation of long-lived metastable negative

ions. For the present study, particular attention is paid to the formation of long-lived anions.

Here we study the properties of negative ions that are created through electron transfer

in collision with potassium atoms in high-lying Rydberg states. Rydberg atoms, atoms in

states of high principal quantum number n, exhibit exaggerated properties. Typically, the

1

2separation between the core ion and the excited electron is such that the target molecule

views the highly-excited atom as two independent scatters.

One of the major benets in utilizing Rydberg atom techniques for studying electron

attachment processes is the extremely low energy of the attaching electron. Its mean kinetic

energy, which is equal to its binding energy, can be varied from a few meV down to eV

by changing the principal number, n, of the atom. The velocity of the electron in its orbit

is high compared to the relative velocity of the atom and the target molecule at thermal

temperatures; thus, the energy (velocity) of the electron dominates the interaction.

1.2 Rydberg Atom Properties

The physical characteristics of Rydberg atoms are quite dierent from those of atoms

in ground or low-lying excited states. This is illustrated by Table 1.1 which lists a number

of atomic properties, their dependence on n, and representative values for each at several

n.

Property scaling(a.u.) n=1 n=15 n=30

Mean radius n2 5.3 109cm 18nm 48nm

Orbital period 2n3 1.5 1016s 0.5ps 4.5ps

Binding Energy 12n2

13.6eV 60meV 15.1meV

Radiative Lifetime 0n3 6.78ns 22.9s 183s

Table 1.1: Properties of Rydberg atoms.

The large size of the Rydberg atom indicates a large separation between the excited

electron and the core ion. For n 10, the separation between the core ion and the excited

3electron is greater than the range typical of either electron/molecule or ion/molecule in-

teractions; therefore, during collision with a neutral target, the Rydberg core and excited

electron act as independent scatters leading to the so-called essentially-free electron model.

Chapter 2

Ion Kinematics in an Ideal Penning Trap

2.1 Introduction

Figure 2.1: Ideal Penning trap with hyperbolic electrodes.

The conning of ions in a trap has been extensively studied since 1936 when Francis

Michel Penning applied an axial magnetic eld to an electric discharge to increase the path

length of electrons [5]. The basic structure of a Penning trap consists of three electrodes: two

end-cap electrodes and a ring electrode, as shown in Figure 2.1 immersed in a homogenous

axial magnetic eld. This axial eld causes ions to move in circular cyclotron orbits conning

them in the radial direction [6]. Axial connement is achieved by applying constant electric

potentials to the electrodes. The superposed E,B elds trap the ion, but introduce another

particle motion due to EB-terms called the magnetron motion. The magnetron motion

is superimposed on the cyclotron motion as seen in Figure 2.2 and ultimately determines

trap lifetime [5].

4

5Figure 2.2: Magnetron motion superimposed on the cyclotron motion.

2.2 Equations of Motion for an Ion in an Ideal Penning Trap

In an ideal hyperbolic Penning trap as shown in Figure 2.1 with endcaps separated by

a distance 2zo and a ring of radius r0, these parameters are related by, r0 =2z0.

For a charged particle in a constant electric eld and a magnetic eld orientated along

the z axis, the scalar potential , and the magnetic eld B are given by,

B = B0z, (2.2.1)

=V

2z2o + r20

(2z2 x2 y2) = 1, (2.2.2)

where V is the potential applied to the endcap electrodes with respect to the ring electrode,

B0 is the magnetic eld strength inside the trap and 1 is the electric potential inside the

trap generated by the endcaps.

The Lorentz force felt by a charged particle of mass m and charge q is,

F = q (E+ v B) , (2.2.3)

6taking the dot product with x, y and z respectively yields,

Fx = mx = q (1 x+ (v B) x) , (2.2.4)

Fy = my = q (1 y + (v B) y) , (2.2.5)

Fz = mz = q (1 z + (v B) z) . (2.2.6)

Using v = (x, y, z) and B = (0, 0, B0) yields,

x = cy +1220zx, (2.2.7)

y = cx+ 1220zy, (2.2.8)

z = 20zz, (2.2.9)

where 0z is the axial frequency,

0z =

4qV

m(r20 + 2z

20

) , (2.2.10)and c is the cyclotron frequency,

c =qB0m

. (2.2.11)

2.2.1 Radial Motion

To determine the radial motion of the ion in the Penning trap, solving the coupled

dierential equations 2.2.7 and 2.2.8 would be necessary as r = xi + yj. Introducing the

variable u dened by,

u x+ iy, (2.2.12)

allows for the decoupling of equations 2.2.7 and 2.2.8. Dierentiating this equation twice

yields,

u = icu+ 1220zu. (2.2.13)

7Using u = eit, the following characteristic equation is obtained,

22 2c + 20z = 0, (2.2.14)

the roots of which are,

=12

(c

2c 220z

). (2.2.15)

If 2c 220z < 0, then u will be characterized by an exponential decay and the ion will no

longer be trapped (i.e., loses its harmonic characteristic). Dening,

01 =2c 220z, (2.2.16)

we obtain two frequencies,

+ =12(c + 01) , (2.2.17)

=12(c 01) , (2.2.18)

where + is the modified cyclotron frequency and is the magnetron frequency. The

general solution of Eq. 2.2.13 is [5],

u = Aei+t +Beit, (2.2.19)

squaring and adding the x and y components of Eq. 2.2.19 gives,

x2 + y2 = |A|2 + |B|2 + 2|A||B| cos . (2.2.20)

Since 1 cos 1, this equation implies that the radial motion of the ion will oscillate

between an outer radius of |A+B| and an inner radius of |AB|.

2.2.2 Axial Motion

The axial motion of the ion can be extracted from Eq. 2.2.9 which represents the equa-

tion of a harmonic oscillator with natural frequency 0z. The particle will therefore oscillate

in the axial direction with frequency given by Eq. 2.2.10.

82.3 Trapping Requirements

From the above analysis, three independent and uncoupled degrees of motion are ap-

parent: cyclotron, magnetron and axial motions. Conditions for trapping an ion in an ideal

Penning trap are [5],

+ c 0z , (2.3.1)

Under realistic conditions, it is sucient that Eq. 2.2.15 be satised,

c >20z. (2.3.2)

What does Eq. 2.3.2 represent in terms of experimental parameters? Using the denitions

of c and 0z the answer is,

V trap->ejection)----

seg fast_adjust rcl inject_voltage ;;initializes electrodes:3,5,16,17 sto adj_elect16 rcl trapping_voltage sto adj_elect17 rcl inject_voltage sto adj_elect05 rcl trapping_voltage sto adj_elect03 ;;finishes the initialization

44

45

rcl switch_time rcl ion_time_of_flight xswitchtime, then trap

rcl switch_time rcl trapping_time add ;;total trap time is rcl ion_time_of_flight ;;switch_time+trapping_time x>y gosub eject ;;if tof> total trap time, then eject

exit ;;when cycle complete, exit

;;---thus ends the fast adjustment routine-----------------------------

;;---this is the inject subroutine that the program will call upon-------

lbl inject rcl inject_voltage ;;this subroutine recalls voltages sto adj_elect05 ;;defined by inject_voltage and rcl inject_voltage ;;trapping_voltage for ion's injection sto adj_elect16 ;;into trap. rcl trapping_voltage sto adj_elect03 rcl trapping_voltage sto adj_elect17 rtn ;;when all is done return to program

;;---this is the trap subroutine that is called upon by the program-----

lbl trap rcl ion_time_of_flight ;;this subroutine performs the trap rcl switch_time ;;ramp and stores it as volt_voltage subtract ;;which is later used in electrode#5 chs ;;-(tof-switchtime) rcl tau_time 1/x ;;1/(tau_time) multiply ;;-(tof-switchtime)/(tau_time) e^x ;;e^(-(tof-switchtime)/(tau_time)) chs ;;-e^(-(tof-switchtime)/(tau_time)) 1 add ;;1-e^(-(tof-switchtime)/(tau_time)) rcl inject_voltage rcl trapping_voltage subtract ;;(inject_voltage-trapping_voltage) multiply ;;(Vin-Vtr)(1-e^(-(tof- switchtime)/(tau_time))) chs ;;-(Vin-Vtr)(1-e^(-(tof-switchtime)/(tau_time))) rcl inject_voltage add ;;Vin-(Vin-Vtr)(1-e^(-(tof-switchtime)/(tau_time))) sto volt_voltage rcl volt_voltage

46

sto adj_elect05 ;;above voltage is stored in electrodes#: rcl volt_voltage ;;5,16 (which is the entrance to the trap). sto adj_elect16 rcl trapping_voltage ;;trapping_voltage is stored inelectrodes#: sto adj_elect03 ;;3, 17 (which is the exit to the trap). rcl trapping_voltage sto adj_elect17 rtn ;;when all is done, return to program

;;---this is the eject subroutine that the program so gladly uses-----

lbl eject rcl trapping_voltage ;;this subroutine switches the exit electrode sto adj_elect16 ;;of the trap from trap mode to ejection mode rcl trapping_voltage ;;electrodes#: 16, 5 stay in trap mode, but sto adj_elect05 ;;electrodes#: 17, 3 switch from trap to rcl ejection_voltage ;;ejection mode (i.e., trapping_voltage sto adj_elect17 ;;->ejection_voltage) rcl ejection_voltage sto adj_elect03 rtn ;;return to program when all is done

seg tstep_adjust ;;this routine adjusts the time step of the rcl ion_time_step 0.01 ;;calculations. x>y exit ;;if 0.01>ion_time_step then exit sto ion_time_step ;;else store the ion_time_step

lbl pe_update rcl update_flag x=0 rtn 0 sto update_flag 1 sto Update_PE_Surface rtn

47

20

1 23

45

6 7

8 9

10111213

1415

16171819

Figure A.1: Electrode numbers for SIMION code reference.

Appendix B

Important Trap Dimensions and Characteristics

B.1 Trap Dimensions and Quantities

z0 = 4cm (B.1.1)

r0 = 4.2cm (B.1.2)

B0 = .3T (B.1.3)

d20 = 12.4cm2 (B.1.4)

D2 = 1.1 (B.1.5)

D4 = 0.1 (B.1.6)

where z0 is one half the trap length, d20 =12

(z20 +

12r

20

),and D2 and D4 are expansion

coecients in Eq. 2.4.1.

V