The status and evolution of plasma wakefield particle accelerators

Transcription

1 The status and evolution of plasma wakefield particle accelerators C Joshi and W.B Mori Phil. Trans. R. Soc. A , doi: /rsta References Rapid response alerting service This article cites 8 articles html#ref-list-1 Respond to this article /577 Receive free alerts when new articles cite this article - sign up in the box at the top right-hand corner of the article or click here To subscribe to Phil. Trans. R. Soc. A go to: This journal is 2006 The Royal Society

2 364, doi: /rsta Published online 24 January 2006 The status and evolution of plasma wakefield particle accelerators BY C. JOSHI* AND W. B. MORI University of California, Los Angeles, CA 90049, USA The status and evolution of the electron beam-driven Plasma Wakefield Acceleration scheme is described. In particular, the effects of the radial electric field of the wake on the drive beam such as multiple envelope oscillations, hosing instability and emission of betatron radiation are described. Using ultra-short electron bunches, high-density plasmas can be produced by field ionization by the electric field of the bunch itself. Wakes excited in such plasmas have accelerated electrons in the back of the drive beam to greater that 4 GeV in just 10 cm in experiments carried out at the Stanford Linear Accelerator Centre. Keywords: plasma acceleration; betatron radiation; hosing instability Although there were four distinct plasma-particle acceleration schemes based on the type of driver pulse used to excite the plasma wake (Joshi & Katsouleas 2003), a consensus is emerging that the highly nonlinear, but also the most robust, blow-out or bubble regime (Barov et al. 1998; Joshi et al. 2002) is probably best suited for reproducible particle acceleration. This regime was first studied in connection with a highly relativistic particle beam driver where the beam density exceeded the plasma electron density. When such a beam propagates through a plasma, the plasma electrons are blown predominantly transversely outward. If the beam is approximately pc/u p long, then these transversely blown out electrons rush back behind the electron beam because of the Coulomb attraction provided by the relatively immobile ions. Here u p is the plasma frequency. The electrons converge on the beam axis to produce a density spike, overshoot and set up a wakefield oscillation. The electron density contours in three dimensions resemble a series of balloons or bubbles; hence, the name the bubble regime (see figure 1). Eventually, the wake becomes turbulent because of phase mixing of the electron orbits. The same process can occur when an intense but short laser pulse propagates through the plasma (Pukov & Meyer-ter-Vehn 2002). In this latter case, it is the transverse ponderomotive force of the laser pulse that expels the plasma electrons rather than the space-charge or Coulomb force of the beam. Since the ponderomotive force acts locally on the plasma electrons, as opposed to the Coulomb force, which can act over a distance of roughly c/u p, the bubble radius * Author for correspondence (joshi@ee.ucla.edu). One contribution of 15 to a Discussion Meeting Issue Laser-driven particle accelerators: new sources of energetic particles and radiation. 577 q 2006 The Royal Society

3 578 C. Joshi and W.B. Mori Figure 1. As a short laser pulse or an electron drive beam is shot through the plasma, it leaves behind it a charge disturbance or a wakefield. In both cases, the beam blows out all the plasma electrons which snap back towards the axis behind the beam. This creates an electron bubble which surrounds both the beam that creates it and the plasma ions that are left behind. The electrical field inside the bubble, shown here with the black curve, resembles an extremely steepened wave that is ready to break. This wave or wakefield can trap some of the electrons from the plasma itself to be accelerated by this field. Alternatively, a distinct trailing electron beam can now be accelerated by the wakefield. is approximately the laser beam radius. In the electron beam case, the bubble radius can be much larger than the electron beam radius. In this paper, we summarize the results obtained thus far on the beam-driven Plasma Wakefield Accelerator (PWFA) scheme. Many phenomena that have been studied in developing this scheme have counterparts in the laser-driven wakefield accelerator scheme. In particular, we focus on three of the important transverse effects that affect both the driver and the accelerating beam: (i) The necessity of matching the beam beta function in vacuum to its value in plasma. (ii) Transverse stability of the drive beam against the so-called hosing instability. (iii) Emission of betatron radiation and its eventual implication at ultra-high energies. 1. Beam matching As mentioned earlier when the beam density, n b, exceeds the plasma density, n p, all the plasma electrons are expelled by the beam. The resulting ion column has a radius r i yðn bo =n p Þ 1=2 s r, where s r is the r.m.s. transverse size of the beam and n bo is the peak beam density. For a Gaussian beam, n bo ZN=ð2pÞ 3=2 s 2 rs z, where s z is the r.m.s. longitudinal length of the beam and N is the total number of particles in the beam. This ion channel exerts a radial focusing force that is linear in r. The radial electrostatic field is given by E r Zð1=2Þn p eð3 o Þr. Here e and 3 o are charge on the electron and permittivity of free space, respectively. This electric field will tend to focus the rest of the electron beam that resides in the ion channel. If the

4 Evolution of wakefield accelerators 579 (a) 300 s x (µm) l=1.4 m s 0 =50 µm e N =12x10 5 m rad b 0 =1.16 m a 0 = 0.5 plasma OFF plasma ON envelope (b) s x (µm) plasma OFF plasma ON envelope equation Fit s=30 µm e N =44x10 5 m rad b 0 =0.11 m a 0 = BetaronFitLongBeta.graph 07250cw Matched Betatron.graph plasma density ( cm 3 ) plasma density ( cm 3 ) Figure 2. The variation of the transverse spot size s x of a 28.5 GeV electron beam on a screen placed 0.5 m downstream of the plasma after the beam has propagated through a LZ1.4 m long lithium plasma as the plasma density is increased. (a) The plasma focusing force is initially larger than the beam emittance force and (b) the beam emittance force is initially larger than the plasma focusing force. s 0 is the initial radius of the beam at the plasma entrance, 3 N is the normalized emittance, a 0 and b 0 are the initial beam parameters. The red points are experimental data and the green curve is the prediction of the envelope equation (1.1) (SLAC Experiments E157, E162). density length product of the plasma is large enough, the electron beam can focus within the plasma itself and indeed undergo multiple focusing oscillations known as betatron oscillations (see figure 2a) of its envelope (Clayton et al. 2002). Clearly, this is an undesirable situation, because the beam exiting the plasma can suffer emittance growth and radiate a significant amount of its energy as betatron or synchrotron radiation, as we shall see later. It is therefore important to match the beam to the plasma such that its radius remains constant as it propagates over many betatron wavelengths. This happens if the beam expansion due to its emittance force is exactly balanced by the focusing force of the ion column. The behaviour of the electron beam with a normalized emittance 3 N is described by the beam envelope equation r ðzþ C k 2 K 32 N g 2 s 4 s r ðzþ Z 0; rðzþ s 00 ð1:1þ where kzu p /(2g) 1/2 c is the restoring constant of the plasma, or equivalently the betatron wavenumber k b. g is the relativistic Lorentz factor and c is the speed of light. The beam is matched if the beam radius is such that b beam Z1/kZb plasma. This matched beam radius r bm is found by setting s 00 (z)z0 leading to r bm Z (3 N /gk p ) 1/2. For a plasma of a given length, if the emittance force initially is larger than the plasma focusing force, the beam radius will oscillate but the amplitude of these oscillations will be reduced, as the plasma density and therefore the plasma focusing force (or equivalently the restoring constant in equation (1.1)) is increased. Figure 2b shows the experimental results on the variation of spot size of the 28.5 GeV electron beam containing 1.4!10 10 electrons after it propagated through an approximately 1.4 m long lithium plasma as the plasma density is increased. The spot size oscillations measured on an external screen damp out as expected, indicating that beam beta function is

5 580 C. Joshi and W.B. Mori (a) without plasma (b) with plasma energy (GeV) head tail x (AU) x (AU) Figure 3. Energy spectra of a s z y50 mm long, 28.5 GeV electron beam with a head-to-tail energy chirp and a tilt (a) without and (b) after going through an approximately 6!10 16 cm K3 density, 30 cm long plasma (SLAC 164 Expt.). As can be seen in (b), the back of the beam shows an exaggerated tilt in the transverse direction x because of energy dispersion. This growth is due to the transverse hosing instability. being matched to that of the plasma at this point. The radiation loss as well as initial noise level for hosing is minimized at this density. 2. The hosing instability Both the laser wakefield and the plasma wakefield accelerators are robust against most parametric type laser plasma or beam plasma instabilities. This is because the drive beam is only about half a plasma wavelength (period) long. However, in both cases there is one transverse instability that can affect the stable propagation of the drive beam. This is the so-called hosing instability (Geraci & Whittum 2000). In the case of the electron beam driver, the hosing instability can lead to the growth of transverse perturbations on the beam due to the nonlinear coupling of the beam electrons to the plasma electrons at the edge of the ion channel through which the beam propagates. As a result, these perturbations grow nonlinearly along the beam leading to transverse break-up of the beam. The differential equations that describe the coupling between the centroid offsets of the beam slice x b and the centroid offset of a pre-formed ion channel x c at a position x within the beam are: v 2 xx b Ckbx 2 b Z kbx 2 ) c ; ð2:1þ v 2 xx c Cu 2 ox c Z u 2 ox b ; p where xzz/ckt, szz and u o Zu p = ffiffi 2. In the asymptotic limit, the displacement x b (s,x) of the longitudinal slice of the beam with an initially linear head-to-tail tilt x o is given by x b Z 0:341 x oðxþ A 3=2 ea cos k b sk A ffiffi 3 p C p 12 ; ð2:2þ

6 Evolution of wakefield accelerators 581 Figure 4. X-ray beam with an energy of approximately 6.5 kev observed 40 m downstream of the plasma. The circular spot is due to betatron emission by the 28.5 GeV electron beam in an approximately 5!10 13 density plasma that is 1.4 m long. The vertical strip is due to bending magnet radiation from a dipole magnet that is used to bend the beam of electrons out of the way (SLAC Experiment E157). where the factor AZð3 3=2 Þ=4½ðk b sþðu o xþ 2 Š 1=3. For instance, for the beam parameters of the ongoing PWFA experiments at Stanford Linear Accelerator Centre (SLAC), gz56 000, n e Z3!10 17 cm K3, xz10 K13 s and sz30 cm, we get x b /x o Z155, a very substantial growth indeed. In fact, even if x o Z10 K2 s r, this amount of growth is larger than the size of the blow-out radius r i given earlier for n bo /n p w1. Fortunately, in the PWFA experiments the hosing growth is found to be substantially less than the predictions of the theory for a preformed ion channel (Dodd et al. 2002). There are several reasons for this, including formation of the plasma by field ionization, non-constant ion channel radius, asymmetric beam sizes and emittances in the two planes, etc. However, all these effects can be modelled using three-dimensional, particle-in-cell (PIC) code simulations. One finds that the hosing growth is substantially less than expected from idealized theory (M. Zhou 2005, personal communication). Figure 3a,b shows two energy spectra of the beam taken using an imaging spectrometer, with and without the plasma. The beam has both a head-to-tail energy chirp (head having greater energy than the tail) and a head-to-tail tilt in the transverse direction. After traversing just a 30 cm long, approximately 6! cm K3 density plasma, the beam energy spectrum is considerably modified. More important, however, in this context is the fact that the tail of the beam not only gains energy, but is also being amplified in its x-tilt. Current experiments are aimed at quantifying the hosing growth and comparing it with theory.

7 582 C. Joshi and W.B. Mori 3. Emission of betatron radiation As mentioned earlier, an unmatched beam undergoes betatron oscillations of its spot size if the plasma density length product is sufficiently large. In a plasma with density n p, the beam with energy gmc 2 will radiate frequencies u r given by 2qg 2 u b u r Z h i; ð3:1þ 1 C a2 2 CðgUÞ2 p where q is the harmonic number, u b Zu p = ffiffiffi 2 g and U/1 is the observation angle from the beam axis. The radiation is emitted in a cone angle approximately a/g, where a is the effective wiggler strength given by azgk b r o which for an ultra-relativistic electron beam can be much less than 1. Furthermore, particles at different radial locations r o have different a and therefore radiate different frequencies. Consequently, for a beam of electrons with a[1, the spectrum typically resembles bending magnet or synchrotron spectrum with a cut-off or critical frequency given by u c Z 3 u2 b 2c g3 r o : ð3:2þ When a 30 GeV electron beam is propagated through a plasma with 10 13! n e (cm K3 )!10 17, the radiated peak lies in the range 10!hn (kev)!10 MeV energy range (Wang et al. 2002; see figure 4). The electron energy loss is found from the relativistic Larmor formula. Using the betatron orbits due to the radial electrostatic potential, the energy loss as a function of distance is given by dw dz Z 1 3 r om e g 2 u 2 ba 2 : ð3:3þ In the ongoing beam plasma wakefield accelerator experiments at SLAC, n e! 3!10 17 cm K3, transverse r.m.s. spot size, s r Z10 mm and the beam energy is 28.5 GeV. Using these parameters and setting r o Zs r, we find that az173 with u c y50 MeV on-axis and an energy loss rate to betatron radiation of 4.3 GeV m K1. It is clear that for any future high-energy physics applications of either the beam or the laser plasma wakefield accelerator, the accelerating beam must be extremely narrow, such that the rate at which the particles energy gain far exceeds the rate at which they radiate away the energy. Recently, we have been considering how the betatron radiation loss might be advantageously used in a future collider. Since one can copiously produce photons in the 10 MeV range, it is natural to ask if these photons can be efficiently converted into e C e K pairs in a thin, high z target. Our calculations show that it is indeed possible to produce a high yield of positrons (up to several e C per incident electrons) using a target that is roughly 0.5 radiation thickness thick and that the conversion efficiency is largely independent of the material (Chao 1998). This idea is currently being tested in our experiments at SLAC.

8 Evolution of wakefield accelerators 583 Figure 5. The energy spectrum of the 28.5 GeV electron beam (a) without and (b) with propagation through a nominally 10 cm long approximately 3!10 17 cm K3 density, lithium plasma. The beam has a head-to-tail energy chirp of approximately 1.5 GeV. After propagation (figure 3b), the bulk of the beam loses up to 4 GeV energy, whereas the tail particles are seen to gain at least 2.5 GeV energy above the energy of the particles in the head of the beam. When the initial chirp is taken into account the energy gain is greater than 4 GeV in 10 cm (SLAC Experiment E164X). 4. High gradient acceleration of electrons Using extremely short electron bunches, s z w35 mm, containing up to 1.5!10 10 electrons per bunch, we were able to generate plasma by using the electric field of the bunch (see figure 5) itself (O Connell et al. 2005). At the optimum density of 3!10 17 cm K3, the excited wakefield had a short enough wavelength to accelerate the particles at the back of the bunch by more than 4 GeV in less than 10 cm of plasma length (Hogan et al. 2005). Up to 8% of the beam particles, containing approximately 240 pc of charge, were accelerated to greater than 1.5 GeV in these experiments. The maximum energy gain was limited by the plasma length, which in turn, had to be made short enough so that the beam line downstream of the magnetic spectrometer could still handle the dispersed beam. 5. Future prospects In the upcoming experiments, the energy acceptance aperture of the beam line has been increased to accept G10 GeV energy changes to the beam. Now it is possible to explore if the energy gain continues to scale linearly with the length of the plasma or if the hosing instability would reduce the energy gain of particles in the tail of the beam. If these experiments continue to show the linear scaling of energy gain with plasma length, we expect to do a two bunch experiment where a distinct second bunch will be injected behind the drive bunch (as shown in figure 1) to demonstrate the high-gradient acceleration with a narrow energy spread.

9 584 C. Joshi and W.B. Mori The authors are indebted to all their colleagues from the E157, 162, 164, 164X and 167 experiments for their contributions to the work described here. This work was partially supported by DOE grant DE-FG02-ER References Barov, N., Conde, M. E., Gai, W. & Rosenzweig, J. B Propagation of short electron pulses in a plasma channel. Phys. Rev. Lett. 80, (doi: /physrevlett.80.81) Chao, A. (ed.) 1998 Handbook of accelerator physics. Singapore: World Scientific. Clayton, C. et al Transverse envelope dynamics of a 28.5-GeV electron beam in a long plasma. Phys. Rev. Lett. 88, (doi: /physrevlett ) Dodd, E. S., Hemker, R. G., Huang, C.-K., Wang, S., Ren, C. & Mori, W. B Hosing and sloshing of short-pulse GeV-class wakefield drivers. Phys. Rev. Lett. 88, (doi: / PhysRevLett ) Geraci, A. A. & Whittum, D. H Transverse dynamics of a relativistic electron beam in an underdense plasma channel. Phys. Plasmas 7, (doi: / ) Hogan, M. et al Multi-GeV energy gain in a plasma-wakefield accelerator. Phys. Rev. Lett. 95, (doi: /physrevlett ) Joshi, C. & Katsouleas, T Plasma accelerators at the energy frontier and on tabletops. Phys. Today, Joshi, C. et al High energy density plasma science with an ultrarelativistic electron beam. Phys. Plasmas 9, (doi: / ) O Connell, C., Barnes, C. D., Decker, F.-J., Hogan, M. J. Iverson, R. H. Krejcik, P., Siemann, R. & Walz, D. R Field ionization of neutral lithium vapor using a 28.5 GeV electron beam. Proc. PAC Conf., Knoxville, TN. Pukhov, A. & Meyer-ter-Vehn, J Laser wake field acceleration: the high nonlinear brokenwave regime. Appl. Phys. B 74, (doi: /s ) Wang, S. et al X-ray emission from betatron motion in a plasma wiggler. Phys. Rev. Lett. 88, (doi: /physrevlett )

10 Evolution of wakefield accelerators 585