linear, it is not difficult to construct a rather general theorem that provides a useful categorization of all accelerators. Specifically, one can show that if a relativistic particle moving in vacuum at constant velocity interacts with any configuration of electromagnetic fields far from all surfaces of dielectrics or conductors, there can be no net acceleration of the particle. In particular, the theorem implies that the very intense electric fields at a laser focus (106 MV/m, a hundred thousand times greater than the accelerating field of the SLAC linac) cannot be used to accelerate extremely relativistic particles.

At first sight it seems surprising that one can accelerate relativistic particles at all. But even relativistic particles do not move with strictly constant velocity, and accelerators can be built with conductors near the beam. As it traverses a medium or passes near conduc

Acceleration Alternatives

An electromagnetic wave in free space cannor accelerare particles traveling in a straight line. There are two classes of alternatives:

1. Slowing the electromagnetic wave: particles go in o straight line.

a. conventional slow-wave structures

b. new slow-wave structures such as "picker fences" c. dielectric slabs

d. passive media

e. plasma medio

2. Bending the particles; electromagnetic wave goes as in free space.

a. wiggling the particles with a static magnetic field

b. wiggling the particles with an electromagnetic wave c. Allowing the particles to undergo cyclotron motion while proceeding longitudinally

tors or dielectrics, an electromagnetic wave slows down, and it can be made to resonate with a traversing particle. In this process, the wave develops a longitudinal accelerating component. Alternatively, we can bend the particles into serpentine trajectories; but this becomes more and more difficult at relativistic energies. A summary of these considerations is presented in the box above, which shows the division of proposed linear accelerators into two categories:

▷ those based on slowing down the electromagnetic accelerating drive

▷ those based on bending the paths of the particles.

We already have many accelerators based upon conventional slow-wave structures (item la). Typically, for electrons, these are disk-and-washer structures-for example the 2-mile-long SLAC linac. New structures (item 1b) are currently being modeled; they will be important at very short accelerating-field wavelengths such as those conveniently obtained from lasers. The exploitation of short wavelengths has also motivated the study of item 1c, dielectric slabs. By passive media (item 1d) we mean polarizable media, such as a gas below breakdown; into this category would fall the inverse Čerenkov-effect accelerator. Plasma accelerators (item le) are very different from conventional accelerators, and we shall see that they have great promise (and, needless to say, great problems).

The second general means of achieving particle-field resonance, namely bending the particles, is also the basis for the free-electron laser. (In an FEL, however, the

PHYSICS TODAY JANUARY 1988 27

particles are being decelerated.) These are "fast-wave devices." That is to say, the walls do not have to be within a wavelength of the particles. Running a free-electron laser backwards would make an accelerator, and such devices have been proposed. However, any accelerator that employs trajectory bending will not be effective at very high energy, because of synchrotron radiation loss. Nevertheless, this limit is rather high-on the order of hundreds of GeV.

I will discuss four novel acceleration schemes, as well as several less radical approaches. The first two novel schemes are active-media devices: a laser-plasma accelerator and a plasma-wake-field accelerator. The other two novel proposals are slow-wave structures: the wake-field accelerator and the pulsed-power linac. In fact, most accelerators are slow-wave structures, and we shall see that within the confines of conventional structures there is still room for considerable variety. I shall consider four such "semiconventional" acceleration schemes.

Laser-plasma accelerator

The laser-plasma accelerator in its first form was the beatwave accelerator invented by John Dawson and Toshi Tajima at UCLA in 1979. They proposed illuminating a plasma with two intense laser beams of angular frequencies w, and w, whose difference is just the natural plasma Oscillation frequency wp. In this resonant condition, the plasma becomes very strongly bunched. That is, it develops a longitudinal density wave, which can then be employed for acceleration. The transverse electromagnetic field, quite ineffective for acceleration, has been converted into a longitudinal wave by this process. The accelerating electrons ride the plasma wave much like surfers. This development of "ponderomotive wells" can also be regarded as stimulated Raman forward scattering.

To determine the effectiveness of this process, and thus to appreciate its great promise, let us estimate the accelerating field one might obtain in a plasma. If the plasma bunches completely, then EL, the longitudinal,

accelerating component of the electric field is given by

eEL

= mcw, = 4nromc2 where e, m and ro are, respectively, the charge, mass and classical radius of the electron, and n is the plasma density. In a plasma, one can obtain densities of 1017 cm-3, so that eE=2x 10 MeV/m. This is a very large gradient indeed!

Now we need to ask to what extent the plasma will bunch. Ponderomotive wave formation can be estimated analytically, and also evaluated numerically by particle simulation. The two approaches agree very well and indicate that bunching is incomplete; the accelerating gradient eEL is reduced by a factor

where E is the field strength of the input laser at frequency w.. In practice, even taking the rise time of the laser into account, e can be as large as 0.7, so that one can expect to achieve very large acceleration fields.

One must make a rather uniform plasma along the length of the accelerator to maintain resonant excitation of the plasma wave. Recently a group at the RutherfordAppleton Laboratory has obtained adequate uniformity in a "long" plasma 8 mm in length."

Plasma stability is the really important point. To avoid ion effects such as "ponderomotive blowout," one must have a very short laser pulse-shorter than the ion plasma period. Even for such short pulses, adverse plasma phenomena such as laser filamentation and laser selffocusing can occur. In order to study these phenomena, two-dimensional particle simulation studies have been performed, supporting the analytic argument that one can probably find parameters that yield beneficial laser selffocusing but no filamentation.

Study has also been made of how one can add acceleration units in tandem. For one unit alone, the accelerated particles will soon pass the bottom of the

waves, and 7, for transferring the wave energy to the accelerating particles. The full efficiency, wp, can easily become quite small.

Experiments have been started on the laser-plasma accelerator, or the more modest goal of generating beat waves, at UCLA, Rutherford-Appleton Laboratory in England and INRS-Energie in Canada. Figure 2 shows the experimental setup at UCLA. The UCLA group, led by Chan Joshi, and the Canadian group, led by Francois Martin, have achieved 10 accelerating gradients of the order of 500 MeV/m. The Canadian group has succeeded in accelerating electrons from 0.6 MeV to 2.5 MeV.

The wake-field accelerator

The wake-field accelerator is based on the observation that an intense beam, passing near a conducting surface, will leave fields behind-a wake. This is a well-known effect that has been calculated and measured in great detail. Generally it is regarded as an adverse effect; intense beams passing through a cavity leave behind a wake that "loads down" a cavity and makes it "droop" in energy.

It was pointed out by Gustav Voss and Thomas Weiland at DESY in Hamburg in 1983 that an accelerator could be based upon use of the wake field." It turns out, however, that if the beam to be accelerated is located in the same region of space as the wake-producing beam, the wake will not be particularly large. What is needed is a "wake-field transformer." Figure 3 shows a possible realization of this concept. A ring-shaped beam of lowenergy electrons passing through a cylindrical conducting structure leaves behind a wake, which is then transmitted radially inward to become a strong accelerating field on the axis, along which the high-energy beam is traveling. In this way one might obtain accelerating gradients of 150 MeV/m. The primary difficulty is to create and control the wake-producing beam. If it is well defined and short in length, it will produce a strong wake. An experiment to prove the principle of this new mechanism is now under way at DESY. First results, in which electrons have indeed been accelerated, demonstrate the validity of this concept.

The plasma-wake-field accelerator

Pisin Chen and his colleagues at UCLA pointed out in 1985 that an efficient way of producing the plasma wave for a laser-plasma accelerator would be to make use of a particle beam.12 One would excite the plasma with an intense bunch train of high-energy electrons rather than by the beat wave of two laser beams. Because intense bunch trains are readily available, it is relatively easy to study this mechanism experimentally, and such work is currently under way in a collaboration between the University of Wisconsin and the Argonne National Laboratory. 13

The plasma-wake-field accelerator is subject to the same restriction I've discussed above for wake-field accelerators in general Because none of the plasmawake-field configurations proposed so far are transformers, the plan is to tailor the driving pulse train so as to make the wake significant and thus achieve strong excitation of the desired plasma wave.

The switched-power linac

The switched-power linac is a slow-wave structure conceptually quite similar to the wake-field accelerator. Both employ a cylindrical geometry and achieve enhancement of the accelerating voltage pulse by means of a radial transmission-line pulse transformer. The difference is that in the wake-field transformer the pulse is created by an intense electron ring, whereas in the switched-power

PHYSICS TODAY JANUARY 1988 29

linac a current pulse would be produced by switchingprobably by a laser pulse on a photocathode. The concept has been conceived and developed by William Willis and his coworkers at CERN and Brookhaven.14

The scheme exploits two ideas in particular: that a distributed power source leads to high power density and thus high accelerating gradients; and that a short puise length implies high peak power, low stored energy and thus limited heating. The high power density requires a high. pulsed charging voltage. High gain requires that the switched energy be very much larger than the laser energy, and high efficiency requires that the switched energy be comparable to the stored energy. Thus the switched-power concept quickly leads to a study of highvoltage breakdown, to the development of a photocathode and its associated laser, and to the problem of aligning the laser with the photocathodes and the disks of the accelerator structure. A scale model. built at CERN. is shown in figure 4. The development program there has been going on for two years. At least another two years will be required to demonstrate one stage of a switchedpower linac.

An alternative to the photocathode switching under consideration at CERN and Brookhaven would be a solidstate switching scheme being studied at the Universities of Rochester and Osaka. There are questions of efficiency, jitter, high-voltage breakdown, lifetime, repetition rates and the like. In particular, the photocathodes would have to operate in the novel situation in which the photon flux is very high and brief and the electric fields on the switch are very strong. Initial studies have achieved photocurrent densities of 10 A/cm2 with surface fields of 0.06 GV/ m (gold-tungsten wire cathodes of 50-μm diameter). Work is now devoted to increasing the field to about 1 GV/m, to obtain 105 A/cm2 with a quantum yield of 10-2. This would represent an order of magnitude increase over present quantum yields.

In the switched-power scheme, as in the wake-field and laser-plasma accelerators, one faces the important question of reproducibility. In linear colliders, one imagines bringing into collision beams that are a fraction of a micron wide. Such extreme beam compression is necessary if one is to obtain useful collision rates with beams that collide only once before they are disposed of. Can these acceleration concepts lead to beams whose jitter from pulse to pulse is much less than a micron? We don't know yet. Conservative people will go with a "conventional linac," where a great deal is known about deflecting modes and jitter. Such people elect to put their inventive talents into developing novel power sources. In the remainder of this article, I will describe some of their efforts.

Two-beam accelerators

Two-beam accelerators have been studied for some years now by our group at the Lawrence Berkeley and Lawrence Livermore Labs and, more recently, by Wolfgang Schnell and his coworkers at CERN.15 The concept is illustrated in figure 5. Instead of many thousands of power tubes arrayed along the length of the accelerator, one would employ a single high-intensity driving beam of low-energy electrons, parallel to the high-energy beam one seeks to accelerate. The idea makes sense because it is rather easy to make high-power beams of low-energy electrons. This same capability is also an important reason for the great interest nowadays in high-power free-electron lasers.

The two-beam scheme is essentially an attempt to miniaturize conventional rf accelerating structures so that one obtains extraordinarily large accelerating gradients with high efficiency. The low-energy driving beam

30 PHYSICS TODAY JANUARY 1988

provides the short-wavelength rf power essential to this miniaturization. We are speaking of wavelengths on the order of 1 cm, in place of the 10-cm microwave power that present-day rf linacs get from klystron arrays.

The driving beam can give up its energy in at least two ways: It can either be passed through an undulator, thus functioning as a free-electron laser, or it can be bunched and passed through resonant "transfer cavities." As it feeds out microwave power along the length of the accelerator, the driving beam's energy can be replenished by pulsed induction-linac modules or superconducting rf cavities placed along its path. Figure 5 shows a two-beam accelerator with FEL undulators and induction-linac units. An induction accelerator is well matched to the requirements of a collider, it produces high peak power for a short pulse length, and it can be pulsed repeatedly.

The generation of rf power in the two-beam accelerator is very efficient over a wide range of frequencies because energy not given up by the driving beam need not be resupplied by the energy-supply system. Thus, the operating efficiency of a two-beam accelerator can be very high-approching 100%.

The two-beam concept offers considerable latitude in the choice of rf frequency; it can thus be chosen for linearcollider considerations rather than by consideration of the availability of power sources. As the rf frequency f is

increased, the energy stored in the accelerator decreases as f-2, because the transverse size of the linac is proportional to the wavelength. Thus the average rf power also scales as f-2 and the operating cost decreases with increasing frequency. The accelerating gradient at which one can operate the linac increases with frequency, roughly as f0.88, because spark breakdown is inhibited as the pulse is shortened in time and the frequency is increased. Thus one can attain a desired electron energy with a shorter linac. The high gradient does, however, require high rf power, which is a major component of the capital cost. But for many schemes the total capital cost, as well as the operating cost, is less for the smaller, highergradient linac.

However, as the linac grows smaller with increasing rf frequency, it becomes ever more difficult to fabricate. Furthermore, adverse wake-field effects in the highenergy beam become more severe. The longitudinal beaminduced wake field scales as f2; the transverse wake as f3. For example, dipole fields, which cause the beam to snake and twist, vary as the inverse cube of linear dimensions;

the harm they do increases like f3.

Putting these diverse considerations together, we currently think that the frequency should be somewhere between 10 and 30 GHz. Our LBL-Livermore group has fabricated a 4-inch-long prototype section of a 30-GHz structure, using a brazing technique that is typically employed for rf linacs. Alternatively, one can use an electroforming process, with the result shown in figure 6. Both methods appear to be acceptable, demonstrating that frequencies as high as 30 GHz (a wavelength of 1 cm) can be employed in a linac. Furthermore, our group has achieved an accelerating gradient of 180 MeV/m in a small (five cell) 35-GHz structure, using Livermore's ELF electron laser facility as the rf power source.

The LBL-Livermore group devoted considerable effort to the FEL version of a two-beam accelerator. Our Livermore colleagues, led by Donald Proznitz and Thadde us Orzechowski, have shown that the FEL is a copious source of microwave power." 16 They have obtained more than 1.8 GW at 35 GHz from the ELF, a 3-meter-long undulator with a 1.1-kA beam of 3-MeV electrons passing