Adiabatic plasma buncher

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 4, AUGUST 2000 1103

Adiabatic Plasma BuncherM. Ferrario, T. C. Katsouleas, Fellow, IEEE, L. Serafini, and Ilan Ben Zvi

Abstract—In this paper, we present a new scheme of injectioninto a plasma accelerator, aimed at producing a high-quality beamwhile relaxing the demands on the bunch length of the injectedbeam. The beam dynamics in the injector, consisting of a high-voltage pulsed photodiode, is analyzed and optimized to producea 20 long electron bunch at 2.5 MeV. This bunch is injectedinto a plasma wave in which it compresses down to 100, whileaccelerating up to 250 MeV. This simultaneous bunching and ac-celeration of a high-quality beam requires a proper combinationof injection energy and injection phase. Preliminary results fromsimulations are shown to assess the potentials of the scheme.

Index Terms—Bunching, injector, plasma accelerator, pulsedphotodiode.

I. INTRODUCTION

SECOND-GENERATION plasma accelerators are expectedto be very demanding in terms of the required bunch length

[1]. This is because the accelerated beam is required to be shortwith respect to the wavelength of the excited Langmuir plasmawave to maintain high beam quality and small energy spread.Because the anticipated wavelength ranges from 100 to 300m,1.5- to 15- m long bunches (rms) are required, with a bunchpopulation of the order of particles and a good emittance,namely, less than 10 mmmrad rms normalized to achieve thecorrect beam matching into the plasma channel (about 100mwide).

Among the photocathode-based injectors [2], the pulsedphotodiode [3] seems a good candidate to achieve very shortbunches, mainly because of the high field gradient that can beapplied on the photocathode surface, in excess of 1 GV/m. It isalso attractive for its compactness and simplicity. The energyof the diode is typically low (e.g., 1–2 MeV) compared withRF guns. We will show how this low energy can be used toadvantage because it allows for longitudinal bunch compressionin the plasma that is not possible at higher energies.

The basic idea of the scheme described in this paper is forthe bunch to undergo one-quarter of a synchrotron oscillation inthe bucket of the plasma wave, with injection on the minimumof the bucket close to the separatrix (zero acceleration phase)and extraction at the resonant energyjust at the median lineof the bucket (maximum acceleration). This phase oscillationin the bucket performs a bunching while it increases the abso-lute energy spread. Later, the relative is damped away.It will be shown that the final beam is fully consistent with the

Manuscript received February 14, 2000; revised March 28, 2000.M. Ferrario is with INFN-LNF, 00044 Frascati, Italy.T. C. Katsouleas is with the University of Southern California, Los Angeles,

CA 90089-0484 USA.L. Serafini is with INFN-Milano, 20133 Milano, Italy (e-mail: luca.ser-

[email protected]).I. Ben Zvi is with Brookhaven National Laboratory, Upton, NY 11973 USA.Publisher Item Identifier S 0093-3813(00)07236-2.

requirements on bunch length for a second generation plasmaaccelerator [1], even though the injected beam is not (i.e., it islonger than the requirement). Such a compression mechanismcan in principle be exploited even with a different injector, e.g.,a radiofrequency gun. However, we should prove the ability ofRF guns to produce 15-m long bunches at 24 pC of charge atenergies of a few MeV , so as to exploit the compression upto its maximum efficiency. In this paper, we explore the use ofa pulsed photodiode for the simplicity and compactness of theapparatus, which allows a very short drift in between the diodeand the plasma channel, minimizing in this way the debunchingeffect caused by space charge.

It is worthwhile to mention that the idea to use a plasma waveto compress or modulate the density of an electron beam is notnew: the plasma klystron concept, presented in [9] is actuallybased on this idea. While the plasma klystron induces a den-sity modulation on a beam that is much longer than the plasmawavelength [9], producing in this way a train of bunchlets, thesystem presented in this paper is expected to produce a singlebunch shorter than the plasma wavelength.

In the second section of this paper, we present a discussionof the beam dynamics in the diode and the drift to the plasmaaccelerator, with emphasis on how to transport the beam withminimum degradation of its quality (in particular, the rms bunchlength and energy spread). The beam dynamics modeling isbased on a time-dependent space-charge code, HOMDYN [4],recently developed in the framework of RF photoinjectors. Thecode allows us to scan quickly over the parameter space, takinginto account at the same time the emittance behavior and thedebunching effect casued by the longitudinal space-charge fieldof the electron bunch. The model underlying the code is sum-marized in Section III, which also presents the results from thesimulations, with particular concern to the adiabatic compres-sion effect occurring when the beam is injected at zero phase (noacceleration). Section IV describes a possible method to controlthe time jitter between the HV pulse in the diode and the laserdriving the plasma wave.

II. THE PULSED PHOTODIODE: A COMPACT INJECTOR

SUITABLE FOR SHORT ELECTRON BUNCH GENERATION

The pulsed photodiode is essentially an accelerating gap ter-minating a coaxial transmission line where a short (few nanosec-onds) high-voltage pulse (1–2 MV) is applied. The system ba-sically consists of three components: a low voltage pulse gen-erator (with a DC source at 25 kV), a Tesla transformer, and ahigh-voltage transmission line with SFswitches to sharpen therise and fall times of the HV pulse.

Because of the short time duration of the pulse and the shortgap of the diode (1–2 mm), it has been experimentally demon-strated [3] that it is possible to hold such high-voltage pulses

0093–3813/00$10.00 © 2000 IEEE

1104 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 4, AUGUST 2000

without breakdown phenomena: very high field gradients, inexcess of 1 GV/m, have been successfully applied at the pho-tocathode surface. The high-voltage pulse can be synchronizedwithin 150 ps to an external laser (this will be later discussed infurther details), so that the device can be operated as a DC pho-toinjector: a metallic photocathode hit by the laser emits photo-electrons during the laser pulse time duration. In this case, thehigh-voltage DC-pulsed electric field plays the role of RF highgradient fields in RF guns. The electron bunch extracted fromthe diode is easily split from the laser beam, illuminating thecathode in many ways: as an example, we can illuminate thephotocathode at an angle (60–70 ) as usually done in S-bandRF guns [2], with proper correction of the laser wave frontsto avoid a tilt between them and the cathode plane (this wouldbring us to an undesirable lengthening of the cathode emissiontime with respect to the laser pulse duration).

Because of such a strong field, we can generate electronbunches at the cathode and accelerate them rapidly up torelativistic velocities (1–2 MeV). This should be done quickly,to freeze the space-charge forces. Of particular concern is thelongitudinal force that tends to introduce a bunch lengtheningthat would be detrimental to the quality of the beam. In view ofthe need for bunches no longer than 10m, and the fact that thecathode spot size is larger than 100m, we have to operate thebeam in the surface-charge regime typical of high aspect ratiobunches that look like thin pancakes. In this regime [5], thelongitudinal space-charge field scales like the inverse square ofthe bunch radius and is very weakly dependent on the bunchlength.

Equation (1) shows a first-order formula [5], giving the finalelectron bunch length (rms value at the diode exit) as a func-tion of the incident laser pulse length , the laser spot sizeat the cathode , the normalized field gradient(where is the field gradient at the cathode), and the nominalbeam peak current

(1)

where

is the space-charge debunching factor ( kA). For highaspect ratios , as typical of cases under discussionhere, and final at the exit of the diode larger than 5, the factor

can be well approximated by[as far as ; the limit of for

very large is ].In the drift following the diode gap, we should expect a fur-

ther debunching produced by the space-charge–induced energyspread, namely, ; this effect can beeven larger than in the diode, because the bunch lengthening canbe expressed, at first order, by .According to these scaling laws, we should, for a given desiredpeak current (or for a given bunch length and charge), tryto maximize the field gradient and the cathode spot size(which is limited anyway by the anode aperture). Minimizingthe drift length is also crucial.

As a particular example, consider a laser pulse of lengthfs (4 m), spot size m, diode gap 2 mm, and

field gradient at the photocathode 1.3 GV/m (so that atthe diode exit), with a bunch charge of 24 pC ( electrons,

A). This leads to a predicted space-charge debunchingin the diode that is modest, 4.2%. The induced en-ergy spread 0.05%, gives a further debunching

m at the end of the 26-cm long drift space to theplasma channel. It will be shown in the final section that thesimulations agree remarkably well with these analytical predic-tions. This points out the need for short laser pulses and highfield gradients to keep the bunch length within the demands ofthe plasma accelerator.

The transverse beam dynamics sets up some other constraintsdealing with the matching of the beam into the plasma wave.The most important issue is the minimum drift length achiev-able compatibly with the need to apply some focusing to obtainthe correct matching. In fact, the diode, having a flat cathode,is equivalent to having a defocusing lens. A curved cathodeshould be avoided because it leads to bunch lengthening causedby electron trajectories of varying lengths emerging from var-ious points on the curved cathode [6]. The rms beam divergenceat the exit is predicted to be

(2)

Here, is the diode gap length, and the expression for the factoris reported in the Appendix. is very close to 1 for

our case of interest, where .According to (2), we conclude that the diode applies a se-

rious defocusing kick to the beam. The source is the first termin the RHS of (2), which is from the radial field lines of the exitaperture close to the cathode. This term is much larger than thespace-charge kick (second term in the RHS), in fact, for the pa-rameters listed above, we obtain mrad mrad. Inorder to overcome such a high beam divergence at the exit ofthe diode, we place a solenoid lens at 11 cm from the cathode,set at 2.5-kGauss peak field. The solenoid must focus down thebeam into the plasma wave accelerator, which requires a beamspot size of about 50m. The simulation results are shown atthe end of the next section.

III. T HE HOMDYN MODEL AND ITS ENHANCEMENT TO

TREAT ACCELERATION IN PLAMA WAVES

Time-dependent space-charge effects play a crucial role in thebeam dynamics of high brightness injectors. A fast running code(HOMDYN) has been developed to deal with the evolution ofhigh-charge, not fully relativistic multibunch beams in RF fieldsof an accelerating cavity, taking into account the field inducedby the beam in the fundamental and higher order modes, and thevariation of bunch sizes caused by both the RF fields and spacecharge. Such a code is also suitable for the present applicationin which instead of an RF cavity, we have an accelerating gapfollowed by a plasma channel.

In modeling the plasma wave, we include the fields of an ex-ternally driven linear plasma wave, but neglect the self-gener-ated wake fields from the beam loading of the plasma wake.

FERRARIOet al.: ADIABATIC PLASMA BUNCHER 1105

Fig. 1. Electron bunch as modeled by the code HOMDYN to calculate thespace-charge field: uniform cylindrical distribution represented byN slices.See text for definitions of the slice coordinatesz , bunch sizesR(t); L(t), andbunch coordinatesz ; z ; z .

This is justified providing the beam load is not too large [7],namely, when the electron numberis such that

pC GeV/mwave area

m

We review in this section the main features of the model, withsome modifications added specifically for the case under study.

The basic approximation in the description of beam dynamicslays in the assumption that each bunch is described by a uni-form charged cylinder, whose length and radius can vary under aself-similar time evolution while keeping a uniform charge dis-tribution inside the bunch. By slicing the bunch in an array ofcylinders (multislices approximation; see Fig. 1), each one sub-ject to the local fields, we also obtain the energy spread and theemittance degradation caused by phase correlation of RF andspace-charge effects.

The longitudinal space-charge fields on axis at a distanceof the th slice from the bunch tail located at, is

given by [6]

where

and is the bunch charge, is the bunch length, is the sliceradius, and is the slice rest frame aspect ratio.

The radial space-charge fields (linear component) of the sameslice, are given by

where

The plasma longitudinal and transverse (linear component)fields are

and

The equations for the longitudinal motion for each slice are

The evolution of each slice radius is described in the time-domain according to an envelope equation, including dampingcaused by acceleration (second term), solenoid focusing (third),RF-focusing (fourth), plasma focusing (fifth), space-charge ef-fects (sixth), image charges from the cathode surface (seventh),and thermal emittance pressure (eigth)

where the dots indicate the derivation with respect to time,

is the solenoid focusing gradient,

is the RF focusing gradient expressed through the linear expan-sion off-axis of the accelerating field

is the plasma focusing gradient,

is the beam perveance, and is the rms normalized thermalbeam emittance.

In order to evaluate the degradation of the rms emittance pro-duced by longitudinal correlation in space-charge and transverseexternal forces, we use the following expression for the corre-lated emittance:

where and the average isperformed over the slices. The total rms emittance will begiven by a quadratic summation of the thermal emittance andthe correlated emittance

The simulations of the system have been carried out choosingthe following set of parameters: the diode is driven by a 1.3-MVHV pulse applied to a 2-mm gap, whereas the laser pulse hittingthe photocathode is 40 fs long (assumed to be flat top in time;note that this is equvalent to a 12-fs rms laser pulse length) andis focused down to a 0.6-mm spot size (hard edge radius of auniform radial intensity profile), extracting 24 pC of charge. Inorder to take under control the large defocusing kick received bycrossing the anode hole (as discussed in Section II), we applya focusing solenoid lens located 11 cm from the cathode with afield amplitude of 2.5 kGauss (peak field on axis). The plasmawave is assumed to have a plasma wavelength of 300 microns,


Fig. 2. Longitudinal dynamics at 0injection phase (no acceleration). Solid line (left scale) represents the rms electron bunch length. Dotted line (right scale)represents the bunch average energy, and dashed line (left scale) represents the rms energy spread.

Fig. 3. Transverse dynamics at 0injection phase (no acceleration). Solid line (left scale) represents the rms electron bunch radius: the scale is set to show thematching into the plasma wave atz = 0:267 (maximum rms radius is 8 mm atz = 0:11). Dashed line (right scale) represents the rms normalized transverseemittance.

radius microns, starting 26.7 cm from the cathodeand extending through 10 cm with an accelerating gradient of 3GV/m. The resonantgammaof the wave is taken to be .

The beam kinetic energy (dotted line), the rms energy spread(dashed line), and the rms bunch length (solid line) are shownin Fig. 2 for the case of injection at zero acceleration phase(i.e., ) into the plasma wave. The injection energyis 2.45 MeV, with a bunch length of 3.5m at the diode exitand 15.5 m at the end of the drift to the plasma wave. Bunchlengthening is caused by the longitudinal space-charge field.The bunching action of the plasma wave, effective at a properinjection phase of 0 (no acceleration), causes a reduction of

the bunch length in opposition to the space-charge effect, witha final equilibrium bunch length of 3m with an energy spreadof 6%. Matching the beam into the strong focusing channel ofthe plasma wave is critical. An example is shown in Fig. 3, indi-cating the rms radius (solid line) and the rms normalized emit-tance (dashed line). The beam is blown up radially to 8-mm rmsradius in the center of the solenoid (11 cm from the cathode)and focused down to 50m into the plasma wave.

It is interesting to notice that an injection at 60assures max-imum acceleration up to 292-MeV exit energy but no bunchingeffect, as shown in Fig. 4, where the final bunch length is 17mat an energy spread of 12%.


Fig. 4. Longitudinal dynamics at 60injection phase (maximum acceleration). Solid line (left scale) represents the rms electron bunch length. Dashed line (leftscale) represents the rms energy spread. Dotted line (right scale) represents the bunch average energy.

IV. CONTROL OF THETIME JITTER BETWEEN THEPLASMA

WAVE AND THE HV PULSE

The acceleration in the plasma wave changes rapidly with theinjection phase of the electron bunch. In order to get a consistentacceleration and small energy jitter (pulse-to-pulse), we mustcontrol the timing of the injection with unprecedented precision.

The attainment of such stability by synchronization of lasersis hopeless. Therefore, we assume that a single laser controls thetiming of both photocathode illumination and plasma wake gen-eration. This still requires attention to minute details in main-taining constant laser path lengths in the system. That includeshighly stable optical component support, covered and temper-ature controlled light pathways, and similar, well-known op-tical-transport practices. This leaves us with the main challengebeing the variation of the electron time-of-arrival.

The variation in the electron timing is caused by theshot-to-shot variation in the accelerating potential. The pulseddiode waveform is timed by spark gaps. The triggering of aspark gap is a statistical process of creating an avalanche. Theuse of special liquids in the spark gap, laser triggering, andadvanced geometry can reduce the jitter to under 1 ns. Becausethe pulse cannot be made absolutely uniform over the entirewaveform, which is approximately flat-top over 1 ns, we haveto deal with pulse-to-pulse acceleration voltage jitter of a fewpercent. Thus, a timing jitter is generated by the time of flightdependence on the voltage.

The time jitter per a fraction of the accelerating voltage jitteris given as the sum of two terms, the jitter in the diode and thejitter in the drift space past the diode.

The first is given as , and the other as. For typical

values of m and , we see that the timingjitter in the diode is of the order of 30 fs per percent amplitudejitter. In a drift of 0.3 m past the diode, the jitter is about 3ps per percent.

In other words, a pulse-to-pulse correction of the order of afew picoseconds is necessary to maintain the electron bunch andthe plasma wave in synchronism.

We propose to correct this jitter by a feedforward scheme.The principle is simple: a pick-up electrode inserted in the high-voltage transmission line will measure the voltage of the diode.The voltage of the pulse is so high that even a weakly coupledprobe will generate enough signal to eliminate the need for anamplifier.

The electric signal will change the path length of the laserpropagating toward the photocathode. The magnitude of thechange is adjusted so that a compensation of the jitter is accom-plished.

To make this possible, it is necessary to design the path lengthof the high-voltage pulse from the measurement point to thecathode to allow enough delay to enable the feedforward adjust-ment. The laser pulse must arrive at the cathode at the same timethat the part of the pulse that produced the path length changearrives.

The laser variable delay line will be composed of opticallyactive material that changes the index of refraction on the ap-plication of an electrical field. The optical path length of a laserbeam in a medium changes dramatically if the medium is highlydispersive at the laser wavelength and the molecular levels con-tributing to the dispersion are shifted. Such an energy level shiftcan be accomplished either by applying an electric field or byeven using the electric field associated with the laser by in-voking the Stark effect. The appropriate choice of the mediumand the magnitude of the field may result in the required pathlength. The major drawback of this technique would be the cor-responding change in the absorption coefficient. The transportloss of the laser will then be a function of the field, which needsto be corrected.

The photocathode laser starts as an IR laser, which is, usu-ally, multiplied to the UV. The calculations that we will present


to establish the principle correspond to the effect in ammonia, ata wavelength of 10.6m, where data have been available. Moreresearch is necessary to identify a proper material and wave-length for UV operation.

Stark shifting of a vibrational–rotational line of ammonia hasbeen done for spectroscopic applications [8]. The ammonia lineshave been shifted in and out of resonance by applying mod-erate electric fields. The fields necessary to tune through res-onance varied, depending on the line in question. A voltageas low as 30 V over 2-mm gap (field of 15 kV/m) is suffi-cient for some lines. This introduces a large change in the re-fractive index and, hence, the path length of the laser to cor-rect for the jitter. Based on data taken from [8], the producedchange in the refractive index as the resonance is shiftedbetween 9.503 m and 9.443 m is – .Therefore, the length required to change the path length by 1ps is s cm/s m.

The imaginary part of the refractive index that affects the ab-sorption changes from 1.459 to 2 in this change of wavelength.

Incidentally, ammonia has also a resonance line in UV at200 nm, where the change in the refractive index is 0.3.If this resonance is used, the required length would be 1 mm.However, it is most likely that there are other material candi-dates.

Concerning the possible breakdown of the laser transportedthrough the cell, it should be noted that the necessary poweris not very high. With the high electric field on the cathodeand using clean copper surfaces, a quantum efficiency of 0.05%was obtained at 100 MV/m, and at the diode’s operating fieldof 1 GV/m, the expected quantum efficiency is 0.5%. At thisquantum efficiency, the necessary laser energy is about 24 nJ,or a power of 1 MW. This is not expected to result in break-down problems over a spot size of about 1 mm.

This example is given just as a demonstration of principle, andmore work is necessary to produce a practical working device.Besides the identification of the optimal resonant Stark effectmaterial, there are some other concerns to be addressed. Theseare listed below as pointers for further research.

The calculation above was made with solid ammonia, wherethe number density is 4 orders of magnitude larger than theatmospheric gas. High-pressure ammonia gas may be used, butbecause the refractive index is directly proportional to the elec-tron density, the length of the ammonia cell would have to beincreased.

What would be the optical quality of this ammonia column,as solid or gas? Can the laser beam quality be maintained afterpassage through this cell?

Stark shift measurements have been done only in gaseous am-monia. Are the results valid in solid ammonia?

How does broadening from pressure and laser intensity affectthe results?

Can the ammonia hold off the large background field of thepulse (besides the ripple used to affect the shift?)

The necessary response time is commensurate with the rateof change of the voltage on the pulsed diode, which is of theorder of tens of one hundred picoseconds. Is the response timeof the molecule to the applied field sufficiently fast?

Fig. 5. Form factorF (�) plotted as a function ofv for the casef(x) =e , i.e., a Gaussian electric field distribution on axis through the diodegap.

Finally, the change in absorption needs to be calculated andcorrected for.

V. CONCLUSION

We have shown by means of a preliminary analysis that aproper injection (by using a specific beam energy and phase)into a plasma wave can relax the demands for beam quality, inparticular, the maximum bunch length and energy spread ac-ceptable at injection, to meet the requirements of second gener-ation plasma accelerators. We found great advantages in the useof pulsed photodiodes as injectors and beam sources, mainly be-cause of their compactness and the very high gradient achiev-able at the photocathode surface.

Other issues have to be more carefully investigated besideswhat has been done for this analysis: wake fields effects in theplasma wave (i.e., beam loading), spatial variation of the plasmawave accelerating gradient from laser envelope, and multipar-ticle effects not addressable with the use of HOMDYN. Theseare topics for future investigations.

APPENDIX

We assume a first-order, linear, on-axis expansion for thestatic accelerating field

where the field form factor on-axis is specified generically bythe normalized function , such that and .

The beam normalized energy at the gap exit will be given by

where the dimensionless quantity representsan effective normalized gap voltage across the gap of length. Recalling that the transverse momentum change through the

gap is and, the beam rms divergence at the gap exit, defined


by under the assumptions of straightelectron trajectories through the gap and laminar beam, will begiven by

where:

The form factor has a relativistic limit, i.e., at ,given by [typically,

implying), ], whereas the limit at very small

is , which is

again a quantity typically of the order of 1 for a well-behavedfunction , as previously specified [implying

].The behavior of the form factor corresponding

to a gaussian electric field distribution on-axis, i.e., for, which is close to that of a flat cathode-flat

anode geometry for the diode gap, is plotted in Fig. 5 versus.

ACKNOWLEDGMENT

The authors thank T. Srinivasan-Rao for stimulating discus-sions on optical feedback mechanisms.

REFERENCES

[1] C. Clayton and L. Serafini, “Generation and transport of ultrashortphase-locked electron bunches to a plasma beatwave accelerator,”IEEETrans. Plasma Sci., vol. 24, pp. 400–408, Apr. 1996.

[2] C. Travier, “RF guns a review,”Part. Accel., vol. 36, pp. 33–75, 1991.[3] T. Srinivasan-Raoet al., “Table top, pulsed, relativistic electron gun with

GV/m gradient,”AIP CP, vol. 398, pp. 730–738, 1997.[4] M. Ferrarioet al., “Multi-bunch energy spead.induced by beam-loading

in a standing wave structure,”Part. Accel., vol. 52, pp. 1–30, 1996.[5] L. Serafini, “The short bunch blow-out regime in RF photoinjectors,”

AIP CP, vol. 413, pp. 321–334, 1997.[6] , “Micro-bunch production with radio frequency photoinjectors,”

IEEE Trans. Plasma Sci., vol. 24, pp. 421–427, Apr. 1996.[7] T. Katsouleaset al., “Beam loading in plasma accelerators,”Part. Accel.,

vol. 21, pp. 81–99, 1987.[8] J. V. Martonchiket al., “Optical properties of NH3 ice from far infrared

to the near ultraviolet,”Appl. Opt., vol. 24, pp. 541–547, 1984.[9] T. Katsouleaset al., “A plasma Klystron for generating ultra-short elec-

tron bunches,”IEEE Trans. Plasma Sci., vol. 24, pp. 443–447, 1996.

M. Ferrario , photograph and biography not available at the time of publication.

T. C. Katsouleas(M’88–SM’91–F’96), photograph and biography not availableat the time of publication.

L. Serafini, photograph and biography not available at the time of publication.

Ilan Ben Zvi , photograph and biography not available at the time of publication.

Documents

Adiabatic plasma buncher