Plasma Density Transition Trapping as aPossible High-Brightness Electron Beam Source

M.C. Thompson∗ and J.B. RosenzweigDepartment of Physics and Astronomy, University of California, Los Angeles, CA 90095

H. SukKorea Electrotechnology Research Institute, Changwon 641-120, Republic of Korea

(Dated: January 13, 2003)

Plasma density transition trapping is a recently purposed self-injection scheme for plasma wake-field accelerators. This technique uses a sharp downward plasma density transition to trap andaccelerate background plasma electron in a plasma wake-field. This paper examines the quality ofelectron beams captured using this scheme in terms of emittance, energy spread, and brightness.Two-dimensional Particle-In-Cell (PIC) simulations show that these parameters can be optimizedby manipulating the plasma density profile. We also develop, and support with simulations, a setof scaling laws that predict how the brightness of transition trapping beams scales with the plasmadensity of the system. These scaling laws indicate that transition trapping can produce beams withbrightness ≥ 5x1014Amp/(m-rad)2. A proof-of-principle transition trapping experiment is plannedfor the near future. The proposed experiment and its status are described in detail.

PACS numbers: Valid PACS appear here

I. INTRODUCTION

In a plasma wake field accelerator (PWFA) a short,high density electron beam is used to drive large am-plitude plasma waves. Accelerating gradients in thesesystems scale with the non-relativistic plasma frequencyωp = (4πnoe

2/me)1/2, where no is the plasma density, eis the electron charge, and me is the electron mass. Itfollows that high gradient PWFA’s have very short pe-riod waves. Accelerating a second beam in such a systemand maintaining its energy spread and emittance requiresinjecting a sub-picosecond beam into the drive beam’swake with sub-picosecond timing accuracy. This is oftenreferred to as witness beam injection, which has neverbeen fully achieved experimentally. All experiments todate that have injected external electrons into acceler-ating plasma waves have used either continuous electronbeams or beam pulses that were long compared to theplasma wave [1–3]. As a result the accelerated electronshad 100% energy spread.

The difficultly of witness beam injection makes it de-sirable to develop a system in which charge is automat-ically load into the accelerating portion of the wake bythe drive beam’s interaction with its environment. Suket al.[4] recently purposed a new self-trapping system forthe use in the blow out regime of PWFA where nb > no

(underdense condition). In this scheme the beam passesthough a sharp drop in plasma density where the lengthof the transition between the high density in region one(1) and the lower density in region two (2) is smallerthan the plasma skin depth k−1

p = vb/wp, where vb∼= c

the driving pulse’s group velocity. As the drive beam’s

∗Electronic address: mct@physics.ucla.edu

wake passes the sudden transition there is a period oftime in which it spans both regions. The portion of thewake in region 2 has lower fields and a longer wavelengththan the portion in region 1. This means that a certainpopulation of the plasma electrons at the boundary willsuddenly find themselves rephased into an acceleratingportion of the region 2 wake. When the parameters arecorrectly set, these rephased electrons are inserted farenough into the accelerating region to be trapped andsubsequently accelerated to high energy.

In this paper, we expand on the original proposed tran-sition trapping system, examining in greater detail theissues of trapped beam quality and scaling of the sys-tem to higher plasma density. We also present a detailedplan for a plasma density transition trapping proof ofprinciple experiment and report on substantial progresstowards realizing this experiment.

II. TRAPPING SCENARIOS

The current development of the idea of plasma den-sity transition trapping centers around the detailed studyof two particular scenarios. The first case uses a highcharge beam to create a very strong blowout of plasmaelectrons in a plasma with a simple step function longi-tudinal plasma density profile. This is the original caseproposed for transition trapping [4]. The second case isoptimized for a proof of principle trapping experiment.This case uses a beam of much more modest charge tocreate a weak blowout, in the high density region, anduses a sloped plasma density profile to enhance chargecapture and reduce energy spread.

2

FIG. 1: Illustration of particle trapping in the strong blowout case. The vertical black line indicates the original position of thedensity transition. Plasma electron particles originating in the high density region are colored black while particles originatingin the low density region are colored grey.

TABLE I: Drive and Captured Beam Parameters in the Strong Blowout Case. Figures for the captured beam are for the coreof the captured beam, which is about 20% of the captured particles, after 12 cm of acceleration.

Drive Beam Captured BeamBeam Energy 50 MeV Beam Energy 56 MeVBeam Charge 63 nC Beam Charge 5.9 nCBeam Duration σt 3 psec Beam Duration σt 161 fsecBeam Radius σr 500 µm Beam Radius σr 112 µmPeak Beam Density 1.2x1014cm−3 Normalized Emittance εx 155 mm-mrad

Total Energy Spread 13%

A. Strong Blowout Scenario

The strong blowout scenario uses the parameters pre-sented in Table I and illustrated in Figure 1. The plasmadensity profile is a simple step function with a constantdensity of nregion1 = 5x1013cm−3 in the high density re-gion and a constant density of nregion2 = 3.5x1013cm−3

in the low density region. The high charge driver pro-duces a very strong blowout, which in turn results in aclear picture of the trapping process.

In order to increase our understanding of the trappingmechanism we preformed a series of simulation with the2D Particle-In-Cell code MAGIC [5] in which the highand low density plasma electron populations are trackedseparately. The results show that the trapping processactually begins in the high density region, as can be seenin Figure 1. As electrons from the low density region areblown out and pushed backward they enter the high den-sity plasma region. There the oscillation of the region 2plasma electrons is accelerated by the higher ion densityand these electrons return to the axis early and mix withelectrons from the high density region. As this mixedconcentration of plasma electrons crosses the boundarybetween the high and low density regions many of theelectrons find themselves in an accelerating phase of thelow density plasma wake and are trapped and acceler-ated.

The properties of the beam captured in this scenarioare listed in the second column of Table I. The cap-tured beam is very short and has a small radius, both

of which originate from the small accelerating volume ofthe accelerating plasma wave. The beam also has a highcharge that results from the very high concentration ofelectrons in the oscillation density spike that are injected.Unfortunately, the captured beam has a significant en-ergy spread that results from the fast variation in theplasma wake-field accelerating gradient where the parti-cles are captured. The beam also has a poor transverseemittance. This is an unavoidable consequence of trap-ping background plasma particles in the strong blowoutregime. The large transverse momenta imparted to theplasma electrons as the drive beam space charge blowsthem out to the side remains with the particles as theyare trapped and accelerated to high energy.

In addition to the undesirable emittance and energyspread properties of the captured beam, this transitiontrapping scenario is also impractical from an experimen-tal stand point. The drive beam parameters listed in thefirst column of Table I are not currently achievable. Forthis reason we began to look at what sort of trappingexperiments could be done with the more modest driverbeams that are available. During this development wealso found ways to improve both the emittance and en-ergy spread of the captured beams.

B. Weak Blowout Scenario

A great deal can be learned about the mechanismand dynamics of density transition trapping by compar-

3

FIG. 2: Illustration of particle trapping in the weak blowout case. This figure is directly comparable with Figure 1. The scaleand particle coloring are identical. Note that the trapping mechanism is essentially the same except that it proceeds moreslowly due to the low plasma density in the down stream region compared to strong blowout case. The weaker blowout alsoleads to much less transverse disturbance in the plasma, which in turn yields lower emittance.

ing the strong blowout case previously described to a casein which a weak blowout is used. Our standard exampleof a weak blowout case is the proof of principle experi-mental case designed for the Neptune Advanced Acceler-ator Laboratory at UCLA [6]. This case was developedand optimized for parameters achievable at the NeptuneLaboratory through extensive simulations with MAGIC.The driving beam parameters of the simulation are shownin Table II. The driving beam has a ramped longitudinalprofile as shown in Figure 3. Ramped profiles of this typemaximize the transformer ratio of the wake field [7] andcan be produced using a negative R56 magnet compres-sor system. We are developing such a compressor systemfor the Neptune Laboratory [8]. While the ramped beamprofile improves performance, it is not critical to thistrapping scenario.

The plasma density profile used in this case is illus-trated in Figure 3. The plasma density profile is tai-lored to maximize the amount of charge captured whilemaintaining an acceptable amount of acceleration. Thefirst cm of the profile reflects a realistic finite rise timefrom zero to the maximum plasma density. After 5 mmof maximum density the transition takes place and thedensity is reduced to 18% of the maximum. This den-sity drop is near the optimum to maximize charge cap-ture. Decreasing the density of region 2 increase thewavelength of the accelerating plasma wave. This hasthe effect of enlarging the volume of the capture regionand enhancing the amount of charge trapped. Loweringthe plasma density also reduces the accelerating gradient,however, reducing the number of initially captured par-ticles that ultimately achieve resonance with the acceler-ating wave. These two effects compete with the chargecapture maximum occurring at nregion2 = 0.18nregion1.This large drop is necessary to ensure adequate chargecapture, which is achieved at the expense of reducingdensity and accelerating gradient in region 2. As canbeen seen from Table II and Figure 3 the electron beamdensity is 2 times larger than the peak plasma density of2x1013cm−3.

In the simulation the transition is approximated as aperfect step function, the validity of this assumption willbe elaborated on later in this paper. Finally, the grad-ual decline in plasma density after the transition slowlyincreases the size of the accelerating wake field region,which reduces the peak gradient but rephases the cap-tured charge toward the peak field of the wake. Thisrephasing both increases the amount of charge trappedand reduces energy spread. Gradually declining posttransition plasma densities have been shown to have sim-ilar benefits in the strong blowout regime [9].

The parameters of the bunch of captured plasma elec-trons are given in Table II. The captured plasma elec-

-3.0p -2.0p -1.0p 0.0 1.0p 2.0p 3.0p0

500

1000

1500

2000

2500

Direction of Propagation

Curre

nt (A

mp)

Time (sec)

0 1 2 3 4 5 60.0

5.0x1012

1.0x1013

1.5x1013

2.0x1013

Dens

ity (c

m- 3

)

Distance (cm)

FIG. 3: Plasma Density (top) and Drive Beam Current (bot-tom) Profiles.

4

TABLE II: Drive and Captured Beam Parameters in the Weak Blowout Case.

Drive Beam Captured BeamBeam Energy 14 MeV Beam Energy 1.2 MeVBeam Charge 5.9 nC Beam Charge 120 pCBeam Duration 6 psec Beam Duration σt 1 psecBeam Radius σr 540 µm Beam Radius σr 380 µmNormalized Emittance εx 15 mm-mrad Normalized Emittance εx 15 mm-mradPeak Beam Density 4x1013cm−3 Total Energy Spread 11%

-5 -4 -3 -2 -1 0 1 2 3 4

1x1013

2x1013

3x1013

4x1013

5x1013

6x1013

Plas

ma

Dens

ity (c

m-3)

z (cm)

FIG. 4: Measured Transverse Density Profile of the PlasmaColumn

trons form a well defined beam of substantial charge thatcan be propagated and detected without major difficulty.The captured beam is also well separated from the drivebeam in energy and should be easy to isolate. If a bi-gaussian beam with σt = 1.5pec is substituted for theramped profile shown in Figure 3 the captured beamparameters remain unchanged except for a 20% loss ofcaptured charge.

III. EXPERIMENTAL PLANS

An experiment is planned for the Neptune labora-tory at UCLA with the parameters presented in Table IIand Figure 3. By modifying an existing pulse dischargeplasma source [10] we have created a plasma column witha peak density of 6x1013cm−3. As shown in Figure 4 theraw plasma column has a gaussian transverse density pro-file and over 6 cm of the plasma has density greater than2x1013cm−3, the required peak density for the trappingexperiment.

Experimental realization of plasma density transitiontrapping depends on the creation of sharp density transi-tions. The limit on the sharpness of the transition neces-sary to produce trapping is set by the trapping condition

kregion1p LTransition < 1. (1)

As can be seen from Figure 5, this is a very strict condi-tion. The turn on of the capture in this regime is nearly

a step function.The creation of a density transition that satisfies this

criteria is a interesting experimental challenge. At highplasma densities, n ≥ 1014cm−3, it will probably be nec-essary to directly create the plasma with the requireddensity profile already built in. This might be accom-plished though photo-ionization using a laser with an in-tensity profile that matches the desired plasma densityprofile or using a uniform laser to ionize a dual densitygas jet. At lower densities such as 1013cm−3, which canbe easily produced using discharges, it is possible to con-sider a simpler method using a masking screen to gener-ate the density transition. The basic concept of operation

High Density Region

Low Density Region

Plasma Flow

Beam Path

Screen

z

x

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0

50

100

150

200

250

1.5 mm

1 mm0.5 mm0 mm

pC

kPregion 1 LTransition

FIG. 5: Top: Simplified diagram of a plasma density tran-sition produced by a obstructing screen. Bottom: Simulateddependence of captured charge on transition length in theproposed experimental case. Each point is marked with thelength of the transition.

5

xθLTrans θ

V||

V⊥

||

tanvv⊥=θ

Plasma Flow Velocities

xθLTrans θ

V||

V⊥

||

tanvv⊥=θ

xθLTrans θ

V||

V⊥

||

tanvv⊥=θ

Plasma Flow Velocities

FIG. 6: Illustration of the transition geometry.

for the masking screen is illustrated at the top of Figure5. Consider a system in which the plasma discharge isseparated from the path of the driver beam. Once theplasma is created in the discharge apparatus it will dif-fuse and flow towards the beam path. If a perforatedmetal foil or grid of wires is placed in the path of theplasma flow it will block a portion of the flow creatinga low density region. Unfortunately, the plasma densitytransition will not remain sharp as the distance from thescreen grows as portrayed in the simple picture of Figure5. In reality the two plasma regions will diffuse into oneanother on the far side of the screen so that the plasmadensity transition will lengthen and blur as the distancefrom the screen edge increases. This process can be quan-tified using a simple model based on the velocities withwhich the plasma diffuses as shown in Figure 6. On thefar side of the screen from the plasma source the highdensity plasma will continue to flow past the screen inthe direction of the bulk plasma flow with a velocity V‖and will begin flowing into the low density region with avelocity V⊥. The sum of these two vectors defines the linewhich marks the end of the transition into the low den-sity plasma region. Symmetry dictates that the start ofthe transition in the high density region can be defined inthe same way so that the total transition length is givenby

LTrans = 2x tan θ = 2xV⊥V‖

. (2)

Since our plasma is weakly magnetized it is reasonableto assume that the parallel and perpendicular plasmaflow velocities are approximately equal. This assumptionleads to the conclusion

V⊥ ≈ V‖ → LTrans = 2x, (3)

which in turn leads to the new trapping condition

x <k−1

p

2. (4)

This new trapping condition for obstructing screensrequires that the drive beam passes within half a plasmaskin depth of the boundary. For a 2x1013cm−3 plasmathe drive beam will have to pass within 600µm of thescreen. This level of pointing accuracy and stability isnot difficult to achieve.

We have explored the validity of this model throughsimulations. We began by looking at MAGIC PIC simu-lations in which a neutral plasma was initialized in halfthe simulation volume and allowed to diffuse through aperiodic series of conduction obstructions into the restof the volume. This is essentially the situation that wewish to create in our discharge plasma source. By plot-ting histograms of the simulation particles contained insmall bands of ∆x at various distances from the edge ofthe obstructions we were able to make predictions of thetransition length at various positions. The results of thisstudy match the prediction of Eq. (3) almost exactly.

We have also begun to experiment with metal screensin our plasma source. By moving a Langmuir probethrough the transition region behind the screen we havemade rudimentary measurements of the plasma transi-tion. Unfortunately, our existing equipment does notallow a precise distance to be set and maintained be-tween the probe tip and the metal screen. This makes adirect comparison between the data and Eq. (3) impossi-ble. The data do, however, appear to be in approximateagreement with Eq. (3) and we are upgrading our equip-ment to make more precise measurements. While giv-ing inconclusive measurements of the plasma transition,these early screen experiments did confirm our ability toreliably set the plasma density behind the screen. In thelimit of thin sheaths, the density of the plasma in thelow density region behind the screen should be related tohigh density plasma by the relation

nlow

nhigh≈ AScreenOpenArea

AScreenTotalArea. (5)

The screen experiments were conducted using a micro-etch perforated stainless steel screen with 152µm diame-ter holes and an open area of 21%. The observed plasmadensity behind the screen was 19.5% of the unfilteredplasma density, which agrees well with Eq. (5). Thismeans that we should be able to produce the densityprofile shown in Figure 3 from the natural gaussian pro-file of the plasma column by varying the open area of thescreen.

Propagating a beam so close to a metallic screen leadsto other difficulties. Interactions with the screen overthe entire length of the low density plasma region willcompletely disrupt the processes of trapping and accel-eration. To circumvent this problem we examined manyalternative geometries and arrived at a solution based ona screen with a solid metal baffle attached to its edge. Asshown in Figure 7 this baffle moves the sharp portion ofthe density transition away from the screen so that thebeam and plasma wake will no longer interact with it.During the trapping process at the transition, however,the beam and wake still interacts with the baffle. Theprimary effect of the baffle is to block a portion of theparticles participating in the plasma wake oscillation, asillustrated on the top in Figure 7.

Simulating the effects of the baffle on particle trappingis a complex problem. The baffle breaks the cylindrical

6

Normal Screen Screen with Baffle

FIG. 7: Artist’s conception of partial blocking of wake parti-cles by the baffle. The prolate spheroid represents the electronbeam and the toroid that partially intersects the screen baffleis the plasma wake.

symmetry of the problem requiring that any simulationsof its effects must be done in three dimensions.

We used the three dimensional version of the PICcode MAGIC to simulate this problem. Unfortunately,MAGIC 3D is not a parallel code, which ultimately lim-ited the accuracy we could obtain in our simulation, butit was the only three dimensional code available to us thatwould allow a conducting boundary to be place near thebeam path in the plasma. We were able to reproduce theresults of our 2D simulations almost exactly with the 3Dversion of the code. We then modelled the same systemwith a metallic baffle at various distances from the beamcenter. The results of these simulations are summarizedin Figure 8. The points in the graph are taken from sim-ulations in which the simulation cells are 0.17k−1

p on aside, which is the maximum resolution we could obtainwith our computing hardware.

Since Eq. (4) indicates that the beam must pass withink−1

p /2 of the baffle edge, the results shown in Figure 8predict an approximate 50% loss of total captured charge.This may not translate into a 50% loss of particles in thebeam core, however, since the large amplitude particlesblock by the baffle are not necessarily the ones that formthe beam core. The 3D simulations lacked the resolutionto resolve this question.

The final issue with the use of screen produced plasmadensity transitions is the rapid growth of the transitionlength with distance from the screen. The growth rateis large enough that there will be a significant transi-tion length gradient over distance spanned by the plasmawake field. The effect of this transition length gradient isunknown, but will soon be examined in simulation. Weexpect this effect to produce another minor but accept-able degradation of the trapping performance.

0.0 0.2 0.4 0.6 0.8 1.0

0

50

100

150

200

250

300

Tota

l Cap

ture

d Ch

arge

(pC)

Distance Baffle Edge to Beam Center (kpregion1Length)

FIG. 8: Effect of the Beam-Baffle Distance on Trapping

IV. DRIVER CHARGE SCALING

While the captured beam parameters presented inTable II are adequate for a first step, proof-of-principletype experiment they are far inferior to the state of theart beams produced in modern photoinjectors. In orderto find a systematic way to improve the captured beamparameters we began to simulate the effects of scaling upthe drive beam charge without altering the rest of theexperiment. The results of these simulation are shownin Figure 9. Increasing the driver charge increases thestrength of the blowout forming a larger amplitude morenon-linear plasma wave. It follows that all the acceler-ating fields in the problem are increased as is the sizeof the accelerating wave. The impact on the capturedbeam is clearly shown in Figure 9. The amount of chargecaptured, the length of the beam, and the emittance allgrow as the driver charge is increased. Although it de-serves more detailed study, simple scaling of the drivercharge appears to lead to bigger captured beams but nothigher quality ones.

V. WAVELENGTH SCALED SOURCES

We have seen the performance of density transitiontrapping in densities n0 ∼ 1013cm−3 in the precedingsections, as well as how the performance changes withdriver charge scaling. It is also interesting to examinehow the captured beams performance scales with plasmadensity or, equivalently, the plasma wavelength. In orderto scale the transition trapping system to a higher plasmadensity nhigh all the charge densities in the system mustbe increased by the ratio,

nhigh/n0, (6)

7

6 7 8 9 10 11 1220

40

60

80

100

120

140

160

180Beam Core Emittance

ε r, n

orm

alize

d (m

m-m

rad)

Driver Charge (nC)6 7 8 9 10 11 12

0.0

500.0p

1.0n

1.5n

2.0n

2.5n Total Captured Beam Core

Capt

ured

Cha

rge

(C)

Driver Charge (nC)

0.072 0.074 0.076 0.078600.0k800.0k

1.0M1.2M1.4M1.6M1.8M2.0M2.2M2.4M2.6M

12 nC10 nC 8 nC 6 nC

Core Particles

Kene

tic E

nerg

y (e

V)

Z (m)0.072 0.074 0.076 0.078

600.0k800.0k

1.0M1.2M1.4M1.6M1.8M2.0M2.2M2.4M2.6M

Z (m)

All Particles12 nC10 nC 8 nC 6 nC

Kene

tic E

nerg

y (e

V)

FIG. 9: Variation of the captured beam parameters with scaling of the driver beam charge in the weak blowout case.

and all the lengths in the system are decreased by theratio,

λp high

λp 0=

k−1p high

k−1p 0

=1/√

nhigh

1/√

n0=

√n0

nhigh, (7)

where λp represents the typical wavelength of oscillationsin the plasma and is equal to the plasma skin depth λp =k−1

p = c/ωpe.If the transition trapping system is scaled in accor-

dance with these ratios, several simple rules can be de-duced to describe the corresponding changes in the cap-tured beam. Since the accelerating gradient Emax in aplasma accelerator grows as

√n0 and momenta p of the

captured particles goes as the product of the force actingon them and the distance through which it is applied, wecan immediately write,

p ∝ Emaxλp ∝ √n0

1√n0

= Constant. (8)

This scaling law applies to both the longitudinal andtransverse particle momenta. Consequently, the emit-tance ε, which is proportional to the product of momentaand the beam size, goes like

ε ∝ λpp ∝ λp. (9)

The emittance of the captured beam improves as the sys-tem is scaled to higher density as a result of the reductionin the transverse beam size.

The amount of charge captured Q depends on boththe available plasma electron density n0 and the volume

of the accelerating portion of the wave, which is propor-tional to λ3

p. This scaling can be written as

Q ∝ n0λ3p ∝ n0(

1√n0

)2λp ∝ λp. (10)

While the captured charge goes down as the plasma wave-length is reduced, the current I remains constant sincethe length of the beam also goes down with the plasmawavelength,

I ∝ Q

λp/c= Constant. (11)

Finally we can combine the scaling laws for emittanceand current to deduce the scaling of the beam brightnessB

B ∝ I

ε2∝ 1

λ2p

∝ n0. (12)

Thus the brightness of electron beams produced usingdensity transition trapping increases linearly with thedensity of the plasma.

These scaling laws were tested using the 2D PIC codeMAGIC. The cases examined are scaled versions of theproof-of-principle experimental case with a slightly largerdriver charge. The results are summarized in Table III.The simulation results follow the scaling laws preciselyin the range studied. At 2x1017cm−3 transition trap-ping can produce an extremely short beam with excellentemittance and a brightness that exceeds state of the artphoto-injectors. The drive beams needed at all densities

8

TABLE III: Simulations of Wavelength Scaling using MAGIC 2D.

Peak Density σt,Driver QDriver σt,Trap QTrap IPeak,Trap εx,norm,Trap Bnorm,Trap

2x1013cm−3 1.5 psec 10 nC 2.7 psec 1.2 nC 163 Amp 57 mm-mrad 5x1010

2x1015cm−3 150 fsec 1 nC 270 fsec 120 pC 166 Amp 5.9 mm-mrad 5x1012

2x1017cm−3 15 fsec 100 pC 28 fsec 12 pC 166 Amp 0.6 mm-mrad 5x1014

LCLS Photoinjector Specification 100 Amp 0.6 mm-mrad 2.8x1014

must be of similar length and approximately one order ofmagnitude greater charge than the beams they capture.The emittance of the driver, however, is irrelevant as longas the driving beam can be focused sufficiently to matchinto the plasma. This means that plasma density transi-tion trapping might be used as an emittance transformerto produce short, low emittance beam from short beamswith high emittances that were produced using extrememagnetic compression or other techniques that producesignificant emittance growth. The feasibility of this ideais still under study and may be enhanced by our effort tofind new scenarios that produce low emittance trappedbeams.

As described previously, plasma density transitiontrapping, at least in the regimes examine so far, producesbeams of large emittance do to the sizeable transversemomenta the plasma particles have at capture. Scalingto higher density improves the emittance by reducing thebeam size rather than reducing the transverse momen-tum. We are continuing to explore alternative transitiontrapping scenarios in an effort to reduce the transversemomentum of the beam further. This may be accom-plished by using drive beams that are wide and or longcompared to the plasma skin depth. The developmentof the technique of foil trapping, which is discussed inthe next section, might also lead to lower transverse mo-menta.

VI. FUTURE DIRECTIONS

In order to proceed beyond a proof-of-principle tran-sition trapping experiment will necessarily require scal-ing to higher plasma densities. This will require improve-ments to both the driver beam and higher density plasmasources with sharp transitions. The production of veryshort, high current electron drive beams is a matter dis-cussed at great length elsewhere. Ideas for producingplasmas with transition that satisfy Eq. (1) at high den-sities n ≥ 1014cm−3 are still in the conceptual phase. H.Suk plans to pursue development of a laser ionized dualdensity gas jet for use in laser wake field driven transi-tion trapping [9]. We have tentative plans at UCLA topursue development of a high density source based onphoto-ionization of Lithium using a laser with step func-tion intensity profile.

In the extreme limit, one can imagine creating an ultra-sharp transition into a plasma by simply replacing thehigh density plasma region in a transition trapping sce-

nario with a solid metal foil. Electrons would be providedfor trapping from the foil via Fowler-Nordheim field emis-sion [11]. Since this situation is much easier to produceexperimentally then sharp plasma density drops, we havebegun to look at the idea closely.

The field values necessary for significant Fowler-Nordeim emission are easy to achieve in current plasmawake-field experiments. N. Barov et al. have producedwake fields ≥ 140MeV/m in a 1014cm−3 plasma atFermilab [12]. In this experiment the drive beam en-ters the plasma through a metal foil, one side of whichis immersed in the plasma and experiences the largeplasma fields. Taking a reasonable value of β ≥ 50 forthe microscope surface field enhancement factor of thefoil, Fowler-Nordheim theory predicts a large emissionJ ≥ 100Amp/mm2 under these conditions. Unfortu-nately, the emission of charge does not guarantee thatthe emitted charge will be trapped and accelerated. Thecharges emitted from the foil due to the plasma wakefields start essentially at rest and must be accelerated toresonance with the wave within the same period of theplasma wake. This is situation is analogous to that inRF photoinjectors and the same dimensionless parame-ter can be used to evaluate the plasma wake’s potentialto capture foil electrons. This parameter, α, is the ratioof the maximum normalized energy gain per unit lengthand the wave number of the accelerating wave.

α ≡ qEmax

kzm0c2=

dγmax

dz

kz, (13)

where kz = ω/vφ. The capture of electrons starting fromrest typically requires α ≥ 1. If we compare the α pa-rameters of the Barav et al. experiment and a standard1.6 cell photoinjector, see Table IV, we see that a plasmawake is not capable of capturing charge from a foil inthis regime since its α is only 0.3. The frequency of theaccelerating wave is too high in comparison to the accel-erating field and the emitted particles can not achieveresonance with the wave.

The peak accelerating field can be increased by increas-ing the driver beam charge. If this is done while holdingthe plasma density constant, the plasma frequency willremain essentially unchanged and α will increase. Thedriver charge can be increased to the point where α > 1and charge is captured from the foil in the plasma wake.If the driver charge in the Barov et al. experiment is in-creased by a factor of ten the α of the system reaches 1.6and charge is captured. The trapping behavior predictedby the α parameter has been verified by initial MAGIC

9

TABLE IV: Comparison of α parameters.

Accelerating Structure Emax frequency vφ α1.6 Cell Photoinjector 80MeV/m 2.856Ghz c 2.6Barov et al. Wake Field Experiment (7 nC) 300MeV/m 90Ghz c 0.3Experiment with High Charge Driver (70 nC) 1.5GeV/m 90Ghz c 1.6

2D simulations. Further work needs to be done to explorethe parameter space of foil trapping and characterize thecaptured beams.

VII. CONCLUSIONS

The theoretical understanding of the basic plasmadensity transition trapping mechanisms are well devel-oped. The quality of the beams produced by transi-tion trapping is also well understood, as are a numberof methods for optimizing the beam quality. We haveshown, through the development of the wavelength scal-ing laws, that at high densities transition trapping canproduce beams with brightness ≥ 5x1014Amp/(m-rad)2.This exceeds the state of the art brightness of modernphotoinjectors. Many variations on the idea of transitiontrapping, such as foil trapping and the use of drive beamsthat are long and or wide compared to the plasma skindepth, remain to be studied.

A detailed plan is in place for a proof-of-principleplasma density transition trapping experiment. This ex-periment will be conducted at low density using density

modifying screens, a technique which we have made sub-stantial progress in developing. The rest of the hardwarenecessary for the experiment is either already in place, orbeing constructed at this time. We plan to conduct thisexperiment in the second or third quarter of 2003.

With further research and refinement plasma densitytransition trapping holds promise as a future high bright-ness beam source. This source may take several formssuch as an automatically timed PWFA injector or an”emittance transformer” used to convert short beamswith poor emittance into short beams with a much lowertransverse emittance.

Acknowledgments

The authors would like to thank T.C. Katsouleasand L. Ludeking for their assistance with the MAGICPIC simulations. The authors also thank Mike Schnei-der, Chris Muller, Soren Telfer, and Ronald Agustssonfor their technical assistance. This work was supportedby the U.S. Dept. of Energy grant number DE-FG03-92ER40693.

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