We have recently demonstrating the doubling of the energy of particles of the ultra-short, ultra-relativistic electron bunches of the Stanford Linear Accelerator Center [1]. This energy doubling occurred in a plasma only 85 cm-long with a density of {approx} 2.6 x 10{sup 17} e{sup -}/cm{sup -3}. This milestone is the result of systematic measurements that show the scaling of the energy gain with plasma length and density, and show the reproducibility and the stability of the acceleration process. We show that the energy gain increases linearly with plasma length from 13 to 31 cm. These are key steps toward the application of beam-driven plasma accelerators or plasma wakefield accelerators (PWFA) to doubling the energy of a future linear collider without doubling its length

/SLAC

/UCLA

Blumenfeld, I.

Clayton, C.E.

Decker, F.J.

Hogan, M.J.

Huang, C.

Ischebeck, R.

Iverson, R.H.

Joshi, C.

Katsouleas, T.C.

Kirby, N.A.

Lu, W.

Marsh, K.A.

Mori, W.B.

Muggli, P.

Oz, E.

Siemann, Robert H.

U., /Southern California

Walz, D.R.

Zhou, M.

Decker, F. J.

Hogan, M. J.

Iverson, R. H.

Kirby, N. A.

Walz, D. R.

Clayton, C. E.

Marsh, K. A.

Mori, W. B.

Katsouleas, T. C.

UNT Digital Library

Work supported in part by US Department of Energy contract DE-AC02-76SF00515SCALING OF ENERGY GAIN WITH PLASMA PARAMETERS IN APLASMA WAKEFIELD ACCELERATORP. Muggli, T.?Katsouleas, E.?Oz, USC, Los Angeles CA, USAI. Blumenfeld, F.-J. Decker, M.J. Hogan, R. Ischebeck, R. Iverson, N. Kirby, R. Siemann, D. Walz,SLAC, Menlo Park, USAC.E. Clayton, C. Huang, C. Joshi, W. Lu, K.A. Marsh, W.B. Mori, M. Zhou, UCLA, Los Angeles,USAAbstractWe have recently demonstrating the doubling of theenergy of particles of the ultra-short, ultra-relativisticelectron bunches of the Stanford Linear AcceleratorCenter [1]. This energy doubling occurred in a plasmaonly 85?cm-long with a density of ?2.6x1017?e-/cm-3. Thismilestone is the result of systematic measurements thatshow the scaling of the energy gain with plasma lengthand density, and show the reproducibility and the stabilityof the acceleration process. We show that the energy gainincreases linearly with plasma length from 13 to 31?cm.These are key steps toward the application of beam-driven plasma accelerators or plasma wakefieldaccelerators (PWFA) to doubling the energy of a futurelinear collider without doubling its length.INTRODUCTIONPlasma accelerators have two great potential advantageswhen compared to conventional, radiofrequencyaccelerators. First, since the accelerating structure issustained by the plasma itself, there are no fabricationissues related to operation at high frequencies (forexample 2.8?THz or a wavelength of 106?μm at a plasmadensity of 1016?cm-3). Second, plasmas can sustain plasmawaves or wakes with extremely large acceleratinggradients, in excess of 10?GV/m. It is therefore importantto explore the possibility of using plasmas to accelerateparticles to multi-GeV energies. In this context, we arestudying a particle beam-driven plasma acceleratorknown as the plasma wakefield accelerator or PWFA.We have demonstrated that large accelerating gradientscan be excited in plasma s by short electron (e-) andpositron (e+) bunches [1,2,3,4]. To lead to a large energygain, these gradients need to be sustained over longplasma lengths. We have set up a PWFA experiment witha variable plasma length in order to study the scaling ofenergy gain with plasma length and density, and todemonstrate that the energy gain increases linearly withthe plasma length.THE PLASMA WAKEFIELDACCELERATORThe PWFA is driven by the ultra-short (?z>10?μm) e-bunches of the Stanford Linear Accelerator Center(SLAC). Individual bunches with ?1.8x1010, 28.5?GeV e-are focused to a transverse size in vacuum ?r of ?10?μmnear the entrance of a lithium (Li) vapor column locatednear the focal point of the SLAC FFTB line. A schematicof the experimental setup is shown on Fig.1. The Li vaporis produced in a heat-pipe oven [5]. The oven consists ofa 3.8?cm diameter stainless steel tube containing a finestainless steel mesh wick and surrounded by hightemperature heaters. The oven is insulated from the beamline high vacuum by 25?μm thick beryllium windowslocated at each end. The oven is initially filled with ahelium (He) buffer gas at a given pressure and solid Li isplaced in the heaters region. The oven is heated until theLi melts and its vapor temperature is equal to that of thebuffer gas. In that “oven mode” the room temperature Heconfines the pure, hot Li column to the hot zone of theoven [6]. The Li density is determined by the buffer gaspressure, and the Li column length by the length of theheater and is adjustable in three lengths Lp=13, 22, 31?cmwhile the location of the column entrance is kept fixed.The length of the Li column is calculated from thelongitudinal temperature profile of the vapor obtained bypulling a thermocouple probe through the oven. Lithiumwas chosen because of the low ionization potential of itsfirst e- (5.392?eV) and the relatively high potential for itstwo subsequent e- (75.638 and 122.455?eV). In previouslong bunch (?z?700?μm) PWFA experiments the plasmawas created through photo-ionization of the Li vapor byan ultra-violet laser pulse [2, 5]. However, in the presentexperiments the transverse electric field of the ultra-shorte- bunches is large enough to field-ionize the first Li e-over a time scale shorter than the bunch duration [7]. TheADK theory for field ionization [8] indicated that fullionization occurs in the volume surrounding the bunchwhere the electric field exceeds ?6?GV/m. With theSLAC bunches full ionization extends over a radius ofmore than 100μm and starts much before the peak of thebunch current. Ionization over a radius larger than theplasma collisionless skin depth (c /? p,  where?p=(nee/?0me)1/2 is the plasma angular frequency) isnecessary for the wake to be similar to that in a pre-formed plasma. Once Li is ionized, the bunch fields expelthe plasma e- from the bunch volume and lose energy tothe plasma wake. When the beam density nb is larger thanSLAC-PUB-13101Contributed to Particle Accelerator Conference (PAC 2007), 6/25/2007-6/29/2007, Albuquerque, NM, USAthe plasma density ne, all the plasma electrons areexpelled from the bunch volume and a pure ion column isleft behind the head of the bunch. The ion columnpartially (ni=ne<nb) neutralizes the relativistic e- bunch,which is in turn focused. In this regime, the focusing fieldof the ion column is given by Er(r)=(1/2)(nee/?0)r leadingto an aberration-free focusing for the core of the bunch.The ion column also acts as restoring force for the plasmae-, which rush back on axis about one plasma wavelengthafter being expelled. They create an on-axis negativedensity spike, which then accelerates the e- in the back ofthe bunch. The linear theory for the single bunch PWFA[9] indicates that, for a bunch with a small radiuscompared to c/?p, the largest accelerating gradient isachieved when the bunch length and plasma density aresuch that k p?z=(?p/c)?z??2, and scales asEacc.?max?110MV(N/2x1010)/(?z(μm)/700)2. Note that in asingle bunch experiment the particle bunch fills all thephases of the accelerating bucket, and a continuum ofenergy loss and gain is observed. In a real acceleratorconfiguration, the plasma wake is driven by a high chargebunch that only loses energy, while a short (<<2?/kp),lower charge witness bunch  is accelerated with a narrowenergy spread. The plasma accelerator therefore providesboth focusing and acceleration for the witness bunch, andthe energy is extracted from the drive bunch through theplasma wake.Figure 1:  Schematic of the experimental setup (not to scale). The bunch incoming energy spectrum (before the plasma)is measured from the synchrotron radiation emitted by e- in a weak vertical magnetic chicane placed in a region of theFFTB line with horizontal dispersion. After the plasma the beam travels through a magnetic spectrometer consisting ofquadrupole and dipole magnets. The energy spectrum is measured again using Cherenkov radiation emitted by particlesin a thin piece of aerogel.EXPERIMENTAL RESULTSIn the experiment, the bunch interacts with the plasmaand is then transported through an magnetic spectrometerconsisting of  a combination of quadrupole  and dipolemagnets. The spectrometer is designed to ensure that inthe y-dispersion direction of the energy measurementplane the beam size ?y is dominated by dispersion and notby the natural beam size associated with its emittance ?y?y=(?y?y+(??E/E0)2)1/2???E/E0,  whe re  ? y=?y?2/?yis the beam beta function in the y-dispersive plane, ?E isthe bunch energy content around the incoming energy E0,and ? is the dispersion in the energy diagnostic plane.This spectrometer removes the ambiguity between energygain and the transverse momentum that can be impartedby the strong plasma focusing force to a possible off-axisbeam tail at the plasma entrance. The bunch energyspectrum is also measured before the plasma using thesynchrotron radiation emitted by the e- in a weak verticalmagnetic chicane placed in a dispersive region of theFFTB. This spectrum allows for the identification ofbunches with similar incoming longitudinal phase space(z-pz) [4]. It is also used to retrieve the bunch currentprofile by comparison with simulation results of thebunch compression process using the code LiTrack [10].Simulation results indicate that the bunches used in thisexperiment have a low current (<2?kA) “trunk” followedby a bi-Gaussian peak with a current in the 6-16?kA (for?1.8x1010?e-/bunch) with an average rms width between20 and 40?μm.Energy spectra measured after plasmas with a densityof ne=2.7x1017?cm-3 and lengths Lp=13?cm, 22?cm, and31?cm obtained with bunches with similar incomingparameters show that the energy gain increases linearlywith the plasma length. The maximum energy gain is?41?GeV after the 31?cm long plasma, or an energy gainof about 12.5?GeV. This energy gain corresponds to anaverage accelerating gradient of the order of ?40?MV/mthat is driven and sustained along the 31?cm long plasma.In these experiments, the energy gain is limited by theplasma length and by the amount of charge that can belost along the beam line section located after the plasma.Measurements with longer bunch and lower plasmadensities indicate that the measurable energy loss islimited by interception of the low energy particles(<24?GeV) along the beam line and on protectioncollimators. The energy loss is expected to be of the sameorder as the peak energy gain. Systematic measurementsindicate that the energy gain scales linearly with the threeplasma lengths available in this experiment (Lp=13, 22,31?cm). This dependency is also observed at plasmadensities that lead to over all lower energy gains [11].These results suggest that the energy of 28.5?GeV e- canbe doubled in a ne=2.7x1017?cm-3, only about 70?cm longplasma. The successful energy doubling experiment wasperformed with 42?GeV bunches to maximize theabsolute energy gain [1]. The energy spectrometer wasalso modified to account for the very broad energyspectrum of the beam after interaction with the plasma[12].IMPLICATIONS FOR AN ENERGYDOUBLERThe results presented in this paper and previouslypublished [1] represent significant steps toward thepossible realization of an energy doubler for a future e-/e+collider, an afterburner scheme proposed [13]: the energygain by e- scales with plasma length and leads to energydoubling over only 85?cm. The unloaded acceleratinggradient is in excess of 40?GV/m and sustained over longplasma lengths. This gradient is larger than the 10-20?GeV value envisaged for the afterburner. In thatscheme the plasma length for energy doubling will be inthe tens of meters range to reach 0.5 to 1?TeV.With the extremely small beam sizes and emittancesneeded to reach the desired collision luminosity, newissues may be a challenge for the plasma afterburner. Forexample erosion of the head of the drive bunch wouldlead to evolution of the wake amplitude and shape alongthe plasma [14]. Motion of the plasma ions induced by thestrong field of the drive bunch could lead to degradationof the emittance of the witness bunch [15,16]. Couplingbetween transverse motion of the plasma e- forming theaccelerating structure and the bunch e- can seed thegrowth of the well known hose instability which couldlimit the energy gain, produce emittance growth or evendestroy the bunches. All these effects will have to bestudied numerically and experimentally. The beam andplasma parameters will have to be chosen carefully tomitigate the deleterious effect associated with theseissues. Future experiments will focus on the accelerationof a witness e- bunch to a narrow energy spectrum anddetailed studies of positron/plasma interaction at the newSLAC beam facility [17].ACKNOWLEDGEMENTSThe authors would like to thank Dr. Peter Tsou of JPLfor the aerogel. Work supported by US DoE undercontracts DE-AC02-76SF00515, DE-FG03-92ER40745,DE-FG03-98DP00211, DE-FG03-92ER40727, DE-AC-0376SF0098 and NSF Grants ECS-9632735, DMS-9722121, PHY-0078715.REFERENCES[1] I. Blumenfeld et al., Nature 445, 741-744 (15February 2007).[2] P. Muggli et al., Phys. Rev. Lett. 93, 014802 (2004).                                                                                               [3] B.E. Blue et al., Phys. Rev. Lett. 90, 214801 (2003).[4] M. J. Hogan et al., Phys. Rev. Lett. 95, 054802(2005).[5] P. Muggli et al., IEEE Trans. on Plasma Science27(3), pp. 791-799 (1999).[6] C. R. Vidal and J. Cooper, J. Appl. Phys., 40, 3370(1969).[7] C.L. O’Connell et al., Phys. Rev. ST-AB 9, 101301(2006).[8] M. V. Ammosov, N. B. Delone, and V. P. Krainov,Sov. Phys. JETP 64, 1191 (1986).[9] S. Lee et al., Phys. Rev. E 61, 7014 (2000).[10] K. L. F. Bane et al., Stanford Linear AcceleratorCenter Report No. SLAC-PUB-11035, 2005(unpublished).[11] P.?Muggli et al., to be submitted.[12] R. Ischebeck et al., these proceedings.[13] S. Lee et al., Phys. Rev. ST Accel. Beams 5, 121301(2002).[14] C.?Huang et al., Proceedings of the 2005 ParticleAccelerator Conference, Knoxville, Tennessee, 2666,(2005).[15] J.B.?Rosenzweig et al., Phys. Rev. Lett. 95, 195002(2005).[16] R.?Gholizadeh et al., these proceedings.[17] R.?Erickson et al., these proceedings.

Scaling of Energy Gain with Plasma Parameters in a Plasma Wakefield Accelerator

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Scaling of Energy Gain with Plasma Parameters in a Plasma Wakefield Accelerator

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