1629373397-425d4de58b7aea127ffc7c337418ea8d (846389), страница 64
Текст из файла (страница 64)
This is formed by injecting aplasma with the right helicity into a flux conserver, as shown in Fig. 10.49.10.3Plasma AcceleratorsIn Fig. 7.17 we saw how a particle can be accelerated by a wave, thus causingdamping of the wave. In 1979 John Dawson, in a paper with T. Tajima, proposedthat this effect could be used to accelerate particles on purpose for experiments on10.3Plasma Accelerators387Fig. 10.49 Formation of a spheromak [E.B.
Hooper et al., Lawrence Livermore National Laboratory Report UCRL-JC-132034]nuclear physics and the structure of matter. Originally, Dawson envisioned accelerating particles traveling at an angle to a wave, as shown in Figs. 10.50, 10.51, thusgaining velocity faster than that of the wave. This idea spawned many experiments,principally in the U.S., Japan, and England, to develop a new type of accelerator. Sofar, only straight acceleration at zero angle has been tried.There were two early ideas on plasma accelerators: beatwave and wakefield.
Inthe beatwave case, two lines of a laser at (ω0, k0) and (ω2, k2) are set to resonate atωp, which is assumed to be much smaller than the laser frequencies. The beatfrequencies areω1 ¼ ω0 ω2 Δω ’ ω pk1 ¼ k0 k2 Δk k pð10:10ÞThis excites a plasma wave with a phase velocity vϕ ¼ ω1/k1 ωp/kp. Since plasmawaves in a cold plasma do not depend on wavelength [Eq. (4.30)], kp is allowed to38810Plasma ApplicationsFig. 10.50 Surfing at an angle to a wave [Google images]Fig. 10.51 Scheme of a surfatron accelerator [T. Katsouleas and J.M. Dawson, Phys. Rev.
Lett.51, 392 (1983)]have the above value. The phase and group velocities of the light waves are givenby Eqs. (4.86) and (4.87), in which to subscript 0 pertains to the light waves. Thusv2ϕ0 ¼ω2pω202¼cþ,k20k201=2;vg0 ¼ c2 =vφ0 ¼ c 1 þ ω2p =ω20ð10:11Þand similarly for ω2. In the usual limit ωp ω0 so that vg0 ¼ dω0/dk0 Δω/Δk,we see from Eqs. (10.10 and 10.11) that vg0 of the light waves is nearly equal tothe vϕ of the plasma wave. This assures that a laser pulse can continue to pushparticles trapped in the plasma wave over long distances.10.3Plasma Accelerators389At high plasma densities the assumption ωp ω0 no longer holds true.
Thecritical density nc at which ωp ¼ ω0 is defined byω2pn 2:ncω0ð10:12ÞThe number nc is a useful one in laser experiments. In terms of nc, Eq. (10.11) canbe writtenvφ ’ vg0 ¼ cð1 n=nc Þ1=2ðn nc Þ:ð10:13ÞFor example, nc 1.0 1025/m3 for the 10.6-μm CO2 laser line, nc 1.21 1025/m3 for the 9.6-μm line, and nc 1.29 1025/m3 for the 9.3-μm line.
The beatfrequency of 3 1012/s between the 10.6- and 9.6-μm lines corresponds to theplasma frequency at n ¼ 1.1 1023/m3. This is a high density that can be producedby a pulsed plasma or even by the laser beams themselves. Beat waves wereproduced at UCLA in 1985, and acceleration of electrons by beat waves in 1993.Figure 10.52 shows two oscillations differing in frequency by 5 % and their beatwave, which has 20 times the wavelength, according to Eq. (10.10).In wakefield acceleration, plasma waves are excited by a short pulse of electronsor photons.
The waves have plasma frequency fp and wavelength λ c/fp, sincedrive pulse travels at v c. If the plasma wave has sufficient amplitude, electronswill be swept up by the wave and accelerated to v c, gaining mass rather thanvelocity in the relativistic limit. It is also possible to inject electrons in the rightphase by photoemission from a solid with a pulsed laser synchronized with thewave (Fig. 10.53).The relativity factor γ of a plasma wave can be expressed simply in terms of ωp:1=2γ 1 v2ϕ =c2ð10:14ÞUsing Eqs.
(10.12) and (10.13), we haveγ ¼ ½1 ð1 n=nc Þ1=2 ¼ ðn=nc Þ1=2 ¼ ω0 =ω p :ð10:15ÞReal experiments involve beams, not the one-dimensional, infinite plane wavesdescribed so far. In two dimensions, one finds that in addition to regions of acceleration and deceleration, the wave has regions of focusing and defocusing. Ascomputers advanced, it was possible to do cell-by-cell computer simulation to seethe nonlinear development. One result is shown in Fig.
10.54. Here, a very short,intense laser or electron pulse is sent through a plasma. The ponderomotive force ofthe pulse ejects all the electrons, leaving a bubble of the slow-moving ions. As thepulse passes, the electrons are attracted back by the ion charge, forming a negativelayer around the bubble and converging into an electron bunch behind the bubble.39010Plasma Applications2.0Amplitude (arb. units)1.51.00.50.0-0.5-1.0-1.5-2.001000200030004000ωt (radians)500060007000Fig.
10.52 The beat wave of two oscillations differing in frequency by 5 %Fig. 10.53 Electrons surfing on the plasma wave behind a drive pulseFig. 10.54 A plasma bubble created by a short laser or electron pulse [adapted from ScientificAmerican, February, 2006]This has not been seen in experiment, but particle acceleration by the wakefieldeffect has been achieved in several countries with the world’s largest lasers. Themost successful of these experiments was done at the Stanford Linear Accelerator10.3Plasma Accelerators391Fig. 10.55 Plot of energyvs.
radius of an electronpulse in vacuum (left) and ina plasma (right) [M.J.Hogan et. al., Phys. Rev.Lett. 95, 054802 (2005)]Center (SLAC) by a team led by C. Joshi of UCLA. Figure 10.55 shows a highlyrelativistic 28.5-GeV electron pulse, 50 femtoseconds long, with 20 kA peakcurrent. Electrons that have lost energy in forming the wake form the tail of thedistribution, and the few electrons that have been accelerated to higher energy bythe wake field are seen at the top. Note that this is not a spatial distribution, since allis traveling a the speed of light.How large can the plasma wave (ωp, kp) get? Consider the linearized Poissonequation with stationary ions:ε0 ∇ 2 ϕ ¼ k2p ε0 ϕ ¼ ene1 eneϕ ¼ ne2 =ε0 k2pð10:16Þwhere n ne1 for this discussion.
The maximum ϕ occurs when n ¼ n0, the background density. Hence,eϕmax ¼n0 e2 m ω2p¼m mc2 ;ε0 m k2p k2pð10:17Þfor highly relativistic waves. Let us defineδ ϕ=ϕmax ¼ n1 =n0 :ð10:18Þ39210Plasma ApplicationsThe magnitude of the plasma-wave E is then given by ω2E ¼ k p ϕ ¼ k p ϕmax δ ¼ δ p m ’ δ ω p mc;e kpeð10:19Þwhere, again, ω p =k p c. Extracting the n dependence, we have 2 1=2 1=2 δm1=21=21=2E ¼ ω p mc ¼ δ men0 c ¼ :096 δ n0 V=m: ð10:20Þn0 c ¼ δee ε0ε0This is an extremely high field. For instance, if n0 ¼ 1024/m3, E is of order 1 GeV/cm.
In principle, this would allow linear accelerators to be shortened by three ordersof magnitude.Wakefield experiments in the 10’s of GeV regime require a preformed plasma toprevent head-erosion of the laser pulse if it has to ionize the plasma also. Such aplasma has to have n > 1016 cm3 over 1 m and have a radius greater than theblow-out radius (Fig. 10.54) of order c/ωp ’ 17 μm. Gases such as Li, Rb, or Cs canbe used, but lithium has the advantage that it has a high second ionization potentialof 75.6 eV, so that Li++ ions can be neglected.
Typically, a plasma of density5 1016 cm3, 1.5 m long, can be created with a 200 mJ laser pulse (4 TW for50 fs). Such target plasmas were developed by K.A. Marsh and C. Clayton at UCLAfor experiments at SLAC. Numerous variations of wakefield schemes have beendeveloped with the aim of producing high quality electron beams with low emittance (transverse momentum). For instance, a low frequency laser, such as CO2 canbe used to form the wake, and a high frequency 800 nm laser used for injection ofelectrons.
Finally, these methods can also be applied to positrons for electronpositron colliders.10.3.1 Free-Electron LasersA related subject is that of the free-electron laser (FEL), which is the opposite ofplasma accelerators in that an electron beam is used to create radiation rather thanvice versa. A diagram of an FEL appears in Fig. 10.56. An array of permanentmagnets, called a wiggler, is shown linearly, though it is usually helical. Arelativistic electron beam is injected from the left and is wiggled by the Lorentzforce from the magnets. It also creates a plasma and waves in the plasma. Withoutgoing into the mathematics, one can see that motion of the beam and the plasma canemit radiation, and when phased properly, this radiation can grow at the expense ofbeam energy.
The depleted beam is caught in the beam dump at the right.10.4Inertial Fusion393Fig. 10.56 Diagram of a free-electron laser (FEL)10.4Inertial FusionIn the 1970s the advent of powerful lasers motivated physicists to explore thepossibility of achieving fusion in short bursts rather than in a steady-state magnetized plasma. Among these were John Nuckolls and Ray Kidder at Livermore (nowLawrence Livermore National Laboratory); Keith Brueckner at University ofCalifornia, San Diego; Keeve “Kip” Siegel in Michigan, and Chiyoe Yamanakain Osaka, Japan. Siegel founded KMS Fusion but died in 1975 while testifying inCongress.
Inertial fusion can also be achieved without lasers with collapsingmagnetized metal “liners” in a z-pinch, or with ion beams, as in Fig. 10.8, but thegreatest progress has been with lasers. The largest such experiment is the NationalIgnition Facility (NIF) at Livermore. This program could not have started withoutthe LASNEX code written by Nuckolls, and laser fusion research still reliessubstantially on computer simulation.10.4.1 Glass LasersIn laser fusion, a fuel pellet is compressed by laser energy to a density ρ ~ 1000times the density of solid DT (0.2 g/cm3), or about 20 times that of lead, andtemperature of order 10 keV. The Lawson criterion for breakeven in laser fusionworks out to beρr 1 g=cm2 ;ð10:21Þwhere r is the compressed radius.
For ρ ¼ 200 g/cm3, r is ~50 μm.There are two ways to achieve laser fusion. In direct-drive fusion, laser energy isdirected as uniformly as possible over the surface of a fuel pellet, as shown inFig. 10.57. The plastic ablator material is heated by the laser light and blasts off,pushing the layer of frozen DT to a density satisfying the Lawson criterion. Toavoid Rayleigh–Taylor instabilities (Fig. 6.11), which would make small dimples39410Plasma ApplicationsFig.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
