Simulation study of a passive plasma beam dump using varying plasma density
K. Hanahoe, G. Xia, M. Islam, Y. Li, O. Mete-Apsimon, B. Hidding, J. Smith
SSimulation study of a passive plasma beam dump using varying plasma density
Kieran Hanahoe,
1, 2, a) Guoxing Xia,
1, 2
Mohammad Islam,
1, 2
Yangmei Li,
1, 2 ¨OznurMete-Apsimon,
3, 2
Bernhard Hidding,
4, 2 and Jonathan Smith School of Physics and Astronomy, University of Manchester, Oxford Road,Manchester M13 9PL, United Kingdom Cockcroft Institute, Sci-Tech Daresbury, Keckwick Lane, Daresbury,Cheshire WA4 4AD, United Kingdom Department of Engineering, Lancaster University, Bailrigg, Lancaster LA1 4YW,United Kingdom Department of Physics, University of Strathclyde, Richmond Street,Glasgow G1 1XQ, United Kingdom Tech-X UK Ltd., Sci-Tech Daresbury, Keckwick Lane, Daresbury,Cheshire WA4 4FS, United Kingdom (Dated: 5 January 2017)
A plasma beam dump uses the collective oscillations of plasma electrons to absorbthe kinetic energy of a particle beam. In this paper, a modified passive plasma beamdump scheme is proposed using either a gradient or stepped plasma profile to maintaina higher decelerating gradient compared to a uniform plasma. The improvement is aresult of the plasma wavelength change preventing the re-acceleration of low energyparticles. Particle-in-cell simulation results show that both stepped and gradientplasma profiles can achieve improved energy loss compared to a uniform plasma foran electron bunch of parameters routinely achieved in laser wakefield acceleration.PACS numbers: 41.75.Fr, 41.75.Lx, 52.65.Rr a) [email protected] a r X i v : . [ phy s i c s . acc - ph ] J a n . INTRODUCTION The safe operation of a particle accelerator requires that the beam be disposed of once ithas been used. This is usually achieved using a dense material such as a metal, graphite orwater. Such a conventional beam dump can stop even a very high energy electron beam ina relatively short distance. For example, the Large Electron-Positron Collider (LEP) used a2 m long aluminium dump to stop a 100 GeV electron beam and the proposed water-baseddump for the International Linear Collider (ILC) is designed to stop a 500 GeV beam in11 m. However, the high density of the stopping medium and high power of the beam leadto a number of disadvantages for a conventional dump. Both proton and electron beamslead to the production of radionuclides in the stopping material . The dump must becapable of absorbing the high power of the beam (18 MW for the ILC) in a small volume,leading to high power density cooling requirements and high temperatures and pressures .The ILC beam dump design would operate at 10 bar and at a maximum water temperatureof 155 ◦ C. In the case of a water dump, decomposition generates hydrogen and oxygen gaswhich must be removed . In addition, structural materials may suffer radiation damageand lose strength, a concern for pressure vessels and windows . These considerations leadto a conventional beam dump being substantially larger than the length over which theyare able to stop their beam may suggest. For instance, the proposed ILC dump will requirea pumping station, water tower, catalytic hydrogen-oxygen recombiner, and deionizer sitedabove ground, connected via pipes to the dump location. A sump is also required to collectany radioactive water that may leak from the dump and ancillary equipment .One proposed alternative to a high density beam dump uses a beam pipe filled with anoble gas at atmospheric pressure, surrounded by iron cladding. With a length of 1000 mthe power deposited per unit length is greatly reduced . Heat can be dissipated by a simplewater cooling jacket at atmospheric pressure and radio-activation is reduced compared tothe baseline ILC design. However, the disadvantage of this scheme is the extremely longlength required to stop a high energy beam and the associated costs of providing space forsuch a dump.Another dump scheme, focused on in this paper, uses a plasma wakefield to decelerate abunch at a high gradient . The plasma beam dump minimizes radio-activation by operatingat a low density even compared to a gas dump, and potentially allows for the recovery of2ome of the beam energy as electricity rather than dissipation as heat . The high decel-erating gradients achievable with high density ultrashort bunches such as those producedby laser wakefield acceleration make plasma beam dumps suitable to complement compactaccelerators with compact beam disposal.In this paper, Section II compares the plasma beam dump with the conventional beamdump. Section III discusses the use of modified plasma profiles to improve the performanceof a passive plasma beam dump and Section IV presents particle-in-cell simulation resultsfor a range of plasma beam dump parameters using fixed beam parameters. II. PLASMA BEAM DUMP AND CONVENTIONAL BEAM DUMPCOMPARED
The stopping power, i.e. the average loss of energy T with distance, of an electronin a neutral medium depends on its energy. At high energies, losses are dominated bybremsstrahlung. The critical energy T c may be defined as the energy at which losses due tobremsstrahlung are equal to losses due to other factors e.g. ionization. The critical energyin MeV is approximated by T c = (800 MeV) / ( Z + 1 .
2) where Z is the atomic number of thestopping material . For high- Z materials such as lead or copper, bremsstrahlung dominatesat any relevant energy. For lower Z materials such as water, bremsstrahlung is dominantabove a few hundred MeV. The stopping power due to radiation is given by : − d T d x = Zα e n e mc ( γ −
1) ln (cid:16) Z − (cid:17) (1)where α is the fine structure constant, m is the incident particle mass, n e is the electrondensity of the stopping material, e is the elementary charge, γ is the relativistic gamma factorand c is the speed of light, with all quantities in CGS units. As long as bremsstrahlung isdominant, the stopping power is linearly proportional to the kinetic energy of the incidentparticles, T = ( γ − mc .In a plasma medium, an electron bunch is decelerated by collective oscillations of theelectrons in the plasma. The plasma wakefield may be excited by the beam itself in apassive beam dump, or excited by a laser pulse in an active beam dump. The plasma maybe preformed or, if the driver is of sufficient intensity, be a neutral gas ionized by the driveritself . A field-ionized plasma would make the passive dump simple and reliable. A passive3eam dump has recently been demonstrated experimentally over a short distance using alaser-accelerated bunch .The passive dump does however suffer from a major limitation of being unable to decel-erate the head of the bunch due to the finite response time of the plasma. This problem canbe addressed by the active beam dump, in which the beam is decelerated by the wakefieldof a laser pulse . An active beam dump however relies on the provision of a laser pulseand accurate synchronization. Without either the dump would fail to stop the beam and abackup dump would need to be available.Recent experimental results have shown that an electron beam can be decelerated by aplasma when initially offset transversely from the plasma column . The electron beam isattracted by the charge imbalance created by the beam’s transverse fields. In a plasma beamdump employing a pre-formed plasma, this phenomenon would allow the requirements onalignment of the bunch and plasma column width to be relaxed, potentially improving thereliability of the dump.The highest decelerating gradients for a given plasma density can be achieved in thenon-linear regime, where the bunch density exceeds the plasma density. The limit on themaximum decelerating gradient is the wave-breaking field E wb , which depends on the elec-tron plasma frequency ω p : E wb = m e c ω p e , (2) ω p = (cid:32) e n p (cid:15) m e (cid:33) , (3)where m e is the electron mass, (cid:15) is the permittivity of free space and n p is the plasmaelectron density, and all quantities are in SI units.The limit of the wave-breaking field for a plasma density of 10 m − can be comparedwith a copper beam dump for an electron beam of 1 GeV. Equation 1 gives an initial averagedecelerating gradient of 5 . − compared with a wave-breaking field of 96 GV m − .The actual decelerating gradient that can be achieved in a plasma depends on the prop-erties of the electron bunch. A short bunch with density higher than the plasma den-sity can achieve a gradient approaching the wave-breaking limit as has been demonstratedexperimentally . 4 II. PLASMA BEAM DUMP SCHEMES
The simplest version of a plasma beam dump is a uniform plasma into which the particlebunch to be decelerated propagates. The head of the bunch will experience no deceleratingfield, while some part of the bunch will experience a maximum decelerating field. After sometime the part of the bunch that experiences the maximum field will become non-relativisticand will fall behind the rest of the bunch until it reaches an accelerating region of thewakefield. The portion of the bunch will then absorb energy from the wakefield and bere-accelerated. This leads to the rate of energy loss of the bunch dramatically decreasingafter a saturation length L sat , as a substantial proportion of the energy lost is reabsorbed.The saturation length for a beam of initial energy T is approximately the propagationlength at which the maximum decelerating gradient E dec decelerates a portion of the beamto non-relativistic velocity: L sat ≈ T eE dec . (4)Wu et al. proposed to use a structured plasma consisting of a series of foils starting after L sat to absorb the low energy particles and prevent them from being re-accelerated . The presenceof thin foils in the path of a high power beam, and the potential for high temperatures andelectric fields in the plasma may lead to damage to the foils. A scheme that achieves thesame result using a plasma-only decelerating medium may be attractive. A. Varying plasma density
As an alternative to the use of foils to absorb low energy particles, the decelerated particlescan be removed from the accelerating region of the wakefield by defocusing. This can beachieved by increasing the plasma density once the bunch has travelled over the saturationlength. The plasma wavelength λ p is related to the plasma electron density n p by: λ p = 2 πc (cid:32) (cid:15) m e e n p (cid:33) ≈ . × / √ n p (5)where all quantities are in SI units. As the density increases the plasma wavelength decreases,effectively shifting the bunch within the wakefield. Half of one plasma wavelength behindthe drive bunch is the region of highest on-axis electron density. If the plasma density isincreased, decelerated particles will pass through a strong defocusing region and be removed5rom the axis. This will prevent their re-acceleration. For a stepped plasma, the change inplasma wavelength is instantaneous and the decelerated particles do not need to pass throughthe accelerating region. For a gradual plasma density increase the decelerated particles willgain energy in the accelerating region prior to being defocused. Figure 1 shows a diagramof the stepped and gradient plasma density schemes. The rate of change with position ofthe plasma wavelength can be calculated for a given plasma profile, by taking the derivativeof λ p (Equation 5) with respect to z . For a linearly increasing plasma density from initialdensity n i to a final density n f over a length L :d λ d z = πc e n f (cid:15) Lm e e n i (cid:16) n f n i zL (cid:17) (cid:15) m e − . (6)In the linear regime, the defocusing region is located λ p / z over which the plasma wavelength changes by1 / T is the average accelerating field E acc multiplied by the propagationdistance. ∆ T = E acc ∆ z = E acc λ (cid:32) d λ d z (cid:33) − , (7)where λ is the initial plasma wavelength at a given position z . The more rapid the changein plasma density, the less energy will be gained by the decelerated particles, however thedensity has to remain low enough to be achievable and to generate a high decelerating field.In this study the density was increased by a factor of ten over the plasma length. Linear andquadratic plasma density changes were considered. Figure 2 shows a plot of the distancerequired for the plasma wavelength to change by λ /
4. A quadratic density profile maintainsthe rate of plasma wavelength change at a higher level compared to a linear density ramp.This will lead to reduced re-acceleration and thus a more effective beam dump.
IV. SIMULATION RESULTS
Two-dimensional simulations of passive beam dump schemes were carried out using theexplicit particle-in-cell (PIC) code VSim . Bunch parameters were chosen to represent abunch that can be generated routinely by laser wakefield acceleration . The bunch hasan rms length of 7 . µ m, rms radius of 20 µ m and charge of 100 pC. The total energy of6IG. 1: Plot illustrating stepped (dashed line) and linear gradient (solid line) plasmadensity schemes. The density is constant over the saturation length L sat and then increasesto ten times the initial density over the remaining length.FIG. 2: Length over which a low-energy particle is accelerated for linear (dashed line) andquadratic (solid line) plasma density increases over a distance L . The singularity in thequadratic case is a result of the assumption that the rate of plasma wavelength change isconstant for each data point, and this is zero at z = 0.the bunch is 0 .
025 J corresponding a bunch which may be generated by a modest laser pulseof 0 .
25 J assuming 10% laser to bunch efficiency . A moderate energy of 250 MeV allowsthe simulation length to be kept short. A 25 cm plasma length allows the deceleration tosaturate and for modified density schemes to be studied. An initial plasma density n i of7 × m − was used, for a range of step lengths and for linear and quadratically increasingplasma density after the saturation length. For the gradient plasma schemes the density wasincreased by a factor of 10 starting from the saturation length and ending at the end of theplasma. The step schemes increased the plasma density by n i for each step. The step lengthrefers to the length of the flat plasma density between each step.FIG. 3: Energy loss with distance for uniform, stepped and gradient plasma densityprofiles. Prior to approximately z = 10 cm all profiles show the same constant deceleratinggradient.Figure 3 shows the change in total beam energy for different dump schemes. The gra-dient scheme proved to provide the greatest energy loss over 25 cm. Figure 4 shows thelongitudinal phase space for a uniform plasma and a 1 cm stepped plasma profile. In eachplot the bunch has propagated 16 . z − ct < − µ m, outside the extent of theinitial bunch, at z = 16 . . γ
8t the peak intensity of the final bunch corresponds to an energy of approximately 75 MeV. (a) (b)
FIG. 4: Longitudinal phase space histogram at z = 16 . γ/m e c and as such isnot accurate for non-relativistic velocities. The color scale gives the sum of macroparticleweight for each bin. (a) (b) FIG. 5: Histogram of energy vs. transverse coordinate at z = 16 . γ of the electron bunch at z = 0 (dashed line) and after 25 cm (solidline) for a linear gradient plasma profile. The y -scale is the sum of macroparticle weight ineach bin. 100 equally-sized bins were used. V. CONCLUSION AND OUTLOOK
Simulation results show that a short, moderate charge electron bunch can lose a largefraction of its energy in a 25 cm plasma. Stepped and gradient plasma profiles are capableof improving energy loss and provide an alternative to the previously proposed foil scheme.Gradient plasma profiles were found to be most effective in improving energy loss, howeverthere was relatively little difference between the linear and quadratic plasma profiles. Theadvantage of the gradient scheme suggests that the energy gain of non-relativistic particleswhile the plasma wavelength changes is not significant for the parameters used. However,this may not be the case when bunch parameters are such that the accelerating gradientis very large. The achievability of the modified plasma density profiles will depend onthe technology used for the source, which will in turn depend on the beam and plasmaparameters. Such considerations will be important if such a passive plasma beam dump isto be experimentally tested in the future.Plasma beam dumps show great promise in both providing compact deceleration to com-plement high-gradient novel accelerators and in reducing the complexity of beam dumpsin conventional accelerators. Although passive plasma beam dumps are not capable of de-celerating the head of the bunch, the rapid reduction in total beam energy would allow10or a conventional beam dump to absorb the remaining energy with greatly reduced radio-activation and cooling requirements.
ACKNOWLEDGMENTS
This work was supported by the Cockcroft Institute Core Grant and the STFC. Theauthors gratefully acknowledge the computing time granted on the supercomputer JURECAat J¨ulich Supercomputing Centre (JSC).
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