CO_{2} LASER TECHNOLOGY FOR ADVANCED PARTICLE ACCELERATORS
I.V. Pogorelsky1, A. Van Steenbergen1, R. Fernow1, W.D. Kimura2,
S.V. Bulanov3
1. Accelerator Test Facility, Brookhaven National Laboratory, 725C, Upton, NY 11973
2. STI Optronics, 2755 Nortup Way, Bellevue, WA 98004
3. Plasma Physics Laboratory, General Physics Institute, Moscow, Russia
Abstract. Shortpulse, highpower CO2 lasers open new prospects for development of highgradient laserdriven electron accelerators. The advantages of l =10 m m CO2 laser radiation over the more widely exploited solid state lasers with l » 1 m m are based on a l 2proportional ponderomotive potential, l proportional phase slippage distance, and l proportional scaling of the laser accelerator structures. We show how a picosecond terawatt CO2 laser that is under construction at the Brookhaven Accelerator Test Facility may benefit the ATF's experimental program of testing farfield, nearfield, and plasma accelerator schemes.
I. INTRODUCTION
Lasers are the sources of the most intense electromagnetic radiation and strongest electric and magnetic fields available for laboratory research. For example, focusing of a terawatt laser beam into a 10m m spot results in intensity of 1018 W/cm2 and, associated with it, an electric field of 30 GV/cm that exceeds by five orders of magnitude fields attainable in conventional particle accelerators. Such capability stimulates a new highenergy physics discipline to emerge: laserdriven highgradient particle accelerators. The primary practical goal is to find an alternative to conventional accelerators in order to build, in the future, more economical highenergy (~TeV) machines, or compact moderateenergy (~GeV) accelerators.
Presently, a variety of acceleration methods are under consideration and study. All laser accelerator schemes proposed so far may be split into three major categories: far electromagnetic (EM) field, near EM field, and plasma accelerators. How to define the border between the first two methods? EM field may be presented as a sum of propagating EM waves
. (1)
When all wave vectors are real, we talk about far field accelerators. For these schemes it is essential that any distances from the source of the field or from any boundary surface are >>l . Otherwise, near field effects come into play.
Fields with imaginary are called near fields. Actually, in this case, we talk about evanescent EM fields vanishing within a l thick layer above the surface.
In the third group of methods, particles are accelerated not by EM fields directly but by electrostatic fields due to the charge separation in laserinduced plasma waves. So far, the record of ~100 MeV over the 0.5 cm distance laser acceleration has been achieved using laser wakefield acceleration (LWFA) in plasma[1].
In general, particle acceleration by a fastoscillating electromagnetic field becomes possible when a relativistic particle moves in synchronism with the phase of the driving field. The long wavelength of a CO_{2} laser helps to meet this requirement. This feature is of particular importance for farfield acceleration schemes, examples of which are the Inverse Cherenkov Accelerator (ICA)[2,3] and Inverse Free Electron Laser (IFEL) accelerator[4,5].
Proposed nearfield accelerator schemes, Grating Linac[6] and Resonant Accelerator[7], are based on the accelerating action of evanescent fields developed near the periodically shaped surfaces under laser irradiation. Since the spatial scale of such structures is comparable with the laser wavelength, these schemes look practical when a CO_{2} or longerwavelength laser is used as the accelerator driver.
Among known plasmabased laser acceleration techniques, selfmodulated LWFA[8] looks presently the most promising. This method requires a so called "relativistically strong" laser beam that satisfies conditions for relativistic selffocusing in plasma. With the CO_{2} laser, this condition may be satisfied at a 100 times lower plasma density than with a 1m m laser of the same power. Another advantage of CO_{2} lasers for plasma accelerators is based on a l 2proportional ponderomotive potential that controls the intensity of the laserinduced plasma wake. Simulations demonstrate a possibility to accelerate electrons by 250 MeV over a 4 cm distance using properly shaped 5 TW CO_{2} laser pulses propagating inside a low density plasma channel[9].
The approach to utilize the longwavelength laser radiation for particle acceleration study is pursued at the ATF where the first terawatt picosecond CO_{2} laser is under construction to study electron acceleration using farfield, nearfield, and plasma acceleration schemes. We discuss here how all these schemes can benefit from using the CO_{2} laser.
Description of the ATF, its current experiment program, and design of the present and upgraded laser system can be found elsewhere[10,11]. Table 1 summarizes the performance characteristics of the ATF primary components: photocathode RF linac and CO_{2} laser system.
TABLE 1. ATF CO_{2} Laser and eBeam Parameters
CO_{2 }Laser (Present) 

Pulse Duration [ps] 
100 
Output Energy [J] 
1 
Output Peak Power [GW] 
10 
Repetition Rate [Hz] 
0.1 
CO_{2} Laser (Upgrade) 

Pulse Duration [ps] 
3 
Output Energy [J] 
~15 
Output Peak Power [TW] 
~5 
Repetition Rate [Hz] 
0.1 
LINAC 

Bunch Duration FWHM [ps] 
0.410 
Electron Energy [MeV] 
50 
Peak Current [A] 
17050 
Electron Energy Spread [%] 
0.2 
Normalized Emittance [mm.mrad] 
0.52 
Repetition Rate [Hz] 
3 
II. FAR FIELD ACCELERATORS
II.1. Inverse Cherenkov Accelerator
In any laser acceleration scheme, the key question is how to maintain synchronism between particles and oscillating electric fields over an appreciable distance. One of the possibilities is when the particle, traveling in medium with velocity b c, is intersected by the EM wavevector at the Cherenkov angle, q , which is described by the condition
. (2)
Here, the inclination of the wavevector is responsible for developing a longitudinal accelerating field component, while the medium is chosen to produce retardation of the phase velocity of the wave to match the speed of electrons. Inverse Cherenkov acceleration is the only example of a first order, far field acceleration process where the particle interacts with a single EM wave.
In the first ICA demonstration at Stanford University[12], a linear polarized, focused Nd laser beam crossed the path of electron beam in the interaction cell filled with hydrogen. The observed energy shift was 50 keV over the 7 cm interaction length.
In a modified scheme[2] (see Fig.1) which is under test at the ATF, we start with a radially polarized beam. By an axicon, the laser beam is converged to the ebeam axis, z, producing a cylindrically symmetrical interference pattern. An amplitude of the longitudinal component of the electric field, which is responsible for electron acceleration, is described analytically by Bessel function of the first kind of the order 0:
, (3)
where is a field amplitude that depends upon the laser intensity distribution at the axicon surface, W(R),
(4)
with z = R/q . The distribution described by Eq.(3) has the maximum along the z axis that defines the acceleration gradient attainable under the phase matching condition, Eq.(2). The radial position of the first minimum in the distribution Eq.(3) is observed at
; (5)
for l =10.6 m m and q =20 mrad, r_{min » }200 m m. In a practice, the parameter r_{min} shall be chosen according to the realistic size of the ebeam, r_{min » }r_{e}, that propagates along the axicon axis. Then, as follows from Eq.(5), the longer l permits to choose the proportionally bigger angle q . Combining this condition with Eqs.(3) and (4), we come to the conclusion: Ez~l 3/2, due to stronger inclination of the laser wavefront to the ebeam propagation.
FIGURE 1. Axicon focusing of radially polarized laser beam in the inverse Cherenkov accelerator
Another advantage of using the relatively longwavelength CO_{2} laser radiation for the ICA scheme is due to the increase of the "phase slippage" distance, L_{slip}, where the accelerating particle stays in partial synchronism with the driving EM field. The expression for L_{slip} comes from the condition , where D b is the electron velocity increase above the b number defined by Eq.(2). Using , we derive
. (6)
For example, for the conditions of the ATF ICA experiment, L_{slip}=20 cm at D g =25 that corresponds to the 12.5 MeV electron acceleration. It becomes evident that the 1m m laser would require much stronger acceleration gradient in order to attain similar net acceleration over the 10 times reduced distance. However, that requirement would be difficult to satisfy considering the above mentioned proportion Ez~l 3/2.
So far, maximum 3.7 MeV acceleration has been measured when ~1 GW CO_{2} laser power was delivered to the interaction region. After the completion of the ongoing ATF CO_{2} laser upgrade to a 3 ps pulse duration, up to 200 GW laser peak power may be delivered into the hydrogen cell prior to gas breakdown or optics damage. MonteCarlo computer simulation of the ICA process shows a possibility of a 100 MeV acceleration demonstration over the 30 cm long interaction range.[13,14] To avoid phase slippage, gradual or stepwise change of the Cherenkov angle will be introduced over the interaction distance. To produce monochromatic accelerated electrons, the short electron bunches should be phased with the peak accelerating field. For this purpose, periodical electron prebunching with the spatial interval equal to the laser wavelength will be produced in the IFEL accelerator section placed upstream the highpower ICA accelerator cell.
II.2 Inverse FEL Accelerator
The IFEL scheme is an example of a second order, far field laser acceleration process. In this case, a second field of a wiggler magnet is used to bring the relativistic particles into a transverse oscillating motion. Thus, transverse EM laser field has a projection of its electrical component along the local direction of the ebeam propagation (see Fig.2). Hence, electric forces may produce an additional kick to the electrons in the direction of their propagation, provided the laser field is in phase with the electron wiggling.
In vacuum, the oscillating electron can not propagate with a phase velocity of light along the direction of the laser beam. Now, synchronism means that the electron should slip exactly one period (or integer number of periods) of the EM wave while traveling a wiggler period, . The synchronism condition at a small angle limit takes the form
(7)
where K is a dimensionless wiggler parameter equal to and  wiggler magnetic field. Hence, the condition Eq.(7) may be satisfied over a long acceleration distance by adjusting wiggler field and period.
FIGURE 2. Principal diagram of the IFEL accelerator
First proposed in 1972 [4], IFEL acceleration has been demonstrated using FEL[15] and a moderatepower CO_{2} laser[16] as drivers.
The goal of the ATF IFEL experiment is further optimization of the accelerator parameters at a higher CO_{2} laser power. The laser beam is guided inside a lowloss sapphire waveguide of a 2.8 mm internal diameter mounted inside the 0.5 mlong wiggler.
Electron spectra obtained during the ATF IFEL experiment show that practically all the electrons are trapped and accelerated. Because of problems with vacuum degradation when the laser is delivered inside the guide, the laser power has been kept below 0.5 GW. Observed acceleration is 2.2%. Further optimization is under way.
Near term plans call for increasing the CO_{2} laser power to 200 GW. This should result in the accelerating gradient of ~100 MeV/m.[5]
IFEL is also expected to be a good buncher. In the mentioned above oncoming ATF experiment, electrons bunched in the IFEL to the period of l will be sent to the ICA interaction cell to demonstrate quasimonochromatic acceleration. A challenge in this experiment is to produce, deliver through the ebeam transport and focusing system, and maintain during the ICA process tiny electron bunches sized to the fraction of l . To achieve this goal with the longwavelength CO_{2} laser is a problem. But with the l » 1 m m, the same may be hardly feasible.
III. NEAR FIELD ACCELERATORS
III.1 Grating Linac
Nearfield laser accelerator scheme illustrated by Fig.3 is based on excitation of an evanescent field when a laser beam is cylindrically focused onto a periodic structure, e.g., diffraction grating. Electrons injected parallel to the surface will be accelerated when moving in phase with standing wave oscillations. This approach is similar to the RF linac, and is therefore known as a Grating Linac[6]. For a relativistic ebeam to satisfy the synchronism conditions, the structure period is nearly equal to the laser wavelength. Thus, a longwavelength CO_{2} laser radiation helps to use reasonably "macroscopic" structures that may be produced by a conventional lithographic etching technique. Taking into account that the evanescent accelerating field is observed within onewavelength distance from the surface, the requirement to the electron beam dimensions are also not as severe as would be with the 1m m laser driver. In addition, the reduced phase slippage at a long wavelength is relevant for this scheme as well.
FIGURE 3. Principal diagram of the grating linac
When a 1 GW CO_{2} laser beam is focused to the 5´ 0.03 mm strip at the "foxhole" structure, 1 GeV/m acceleration is predicted[17]. Using a short, picosecond laser pulse is a way to avoid the optical damage of the structure. To ensure the interaction of the ebunch, directed perpendicular to the laser beam, over the appreciable acceleration distance (much longer than the laser pulse length), a linear delay shall be introduced across the laser intensity front. It may be done by reflecting the laser beam from the diffraction grating prior to cylindrical lensing.
III.2 DielectricLoaded Resonant Laser Accelerator
In another proposed nearfield electron accelerator scheme[7], linearly polarized laser radiation penetrates through the periodically modulated dielectric structure filling the gap of the FabryPerot interferometer as shown in Fig.4. At the high quality factor of the interferometer cavity, Q, equal to the number of the optical double passes required to reach the field saturation in the cavity, a large stored EM energy and field amplitude can be obtained at the relatively low input laser power. Periodic modulation of the permittivity, e , within the dielectric masks sandwitched between the interferometer mirrors
(8)
ensures a spaceperiodical modulation of the field phase in the central vacuum gap, provided the gap width is of the order of the laser wavelength. The electron beam, propagating inside the vacuum gap in the direction of the laser beam polarization, experiences acceleration due to the synchronously oscillating electric field. The average accelerating field is
, (9)
where I is the incident laser intensity. The accelerating field in excess of 1 GV/m has been estimated for the realistic experimental parameters.
Similar to Grating Linac, this scheme looks more practical with the relatively longwavelength CO_{2} laser, provided the problem of laser damage of the structure is solved.
Figure xxxxxxxxxxxxxxxxxxxxxxxxx
It looks logical to use a highpower CO_{2} laser, which is a strong ionizer, in the schemes where such ionization and related effects are not problems but are desirable, as it happens in plasma accelerators.
An EM wave packet propagating in plasma ponderomotively separates charges initiating their oscillation at the plasma frequency, w _{p}, that depends upon the electron density, N_{e}, by
. (10)
Plasma wave follows the laser pulse with a phase velocity equal to the group velocity of the laser pulse, , where is a plasma refractive index.
A relativistic particle propagating together with plasma wave will experience acceleration until it slips out of synchronism over the distance
. (11)
Initiated via oscillation of free plasma electrons in the laser field, amplitude of a plasma wave is proportional to the energy of the electron oscillatory motion called ponderomotive potential
, (12)
where is the laser field amplitude. This quadratic dependence of the ponderomotive potential upon the laser wavelength makes CO_{2} laser an attractive candidate to drive plasma accelerator.
Amplitude of the accelerating field due to the longitudinal charge separation depends upon the particular method of the plasma wave excitation.
In the LWFA scheme, plasma waves are initiated by an instant "shock" that is produced with a short laser pulse optimally equal in duration to the halfperiod of the plasma wave, . Note, that after developing a highpower picosecond CO_{2} laser, there will be the firsttime opportunity to use CO_{2} laser in this scheme in a practically meaningful range of the plasma density, Ne=10141015 cm3. The advantage of using CO_{2} laser in the LWFA scheme stems from the proportionality of the accelerating field to the laser wavelength that is the result of the strong ponderomotive potential in the CO_{2} laser field and, in particular, follows from the expression[8]
, (13)
where (14)
is the dimensionless laser strength parameter.
In the laser beatwave accelerator (LBWA) scheme we choose periodical force that matches the plasma frequency and resonantly enhances plasma oscillations. Such laser intensity modulation is produced by mixing two laser beams of different frequencies that satisfy a condition .
The accelerating field in the LBWA reaches an amplitude of
. (15)
Thus, due to the proportion of (see Eqs.(14) and (15)), CO_{2} laser can produce 6 times stronger acceleration than a 1m m laser of the equal intensity.
Exploiting this feature, up to 30 MeV acceleration over a 1 cm interaction distance has been demonstrated using subnanosecond, multigigawatt, dualwavelength CO_{2} lasers.[18,19] The expected enhancement of the acceleration gradient with a picosecond terawatt CO_{2} laser is due to higher strength parameter entering Eq.(15) and higher stability of the fastexcited wakefield.
The third, selfmodulated (SM) LWFA scheme, looks the most promising. It comes to the scene when the laser pulse is relativistically strong. Relativistically strong means that laser power, P, satisfies the condition of relativistic selffocusing
. (16)
In this case, initially small plasma density oscillations cause modulation at the plasma frequency of the laser beam envelope and its intensity. Then, the pulse resonantly enhances the plasma oscillation similar to the LBWA scheme matched automatically to the local plasma density. It is understood that the laser pulse length in this case shall extend over several plasma periods, .
It has been shown by simulations that, if the laser pulse is just strong and long, it is still not enough to produce an intense and regular wake[9]. The wake needs an efficient initiation, similar to that provided in the LBWA or LWFA schemes. One of the possibilities is when a steep leading front, with , serves as a good initiator for a plasma wave. Simulations done for a 5TW, 1.5ps, appropriately shaped CO_{2} laser pulse propagating in a plasma channel[9] predict electron acceleration to 250 MeV.
Finally, let us address the question of how to compare potential performance of 10m m and 1m m lasers in the SMLWFA configuration. An accelerating field attainable at the plasma wave breaking limit is
. (17)
According to Eq.(14), a is proportional to l . In spite of this fact, the expression for the net acceleration
, (18)
obtained from Eqs.(11) and (17), still seems beneficial for shorter wavelength lasers. However this first impression is misleading. The thing is that, for the SMLWFA scheme, the choice for parameters entering Eq.(18) is not arbitrary. The values of w and w _{p} are linked together through the selffocusing condition, Eq.(16).
Assume for our wavelength comparison two laser beams of the equal power but different wavelength, both close to the relativistic selffocusing condition, and focused to the equal spot size. Then, the ratio w /w _{p} should be chosen equal for any laser wavelength. The result of it is that the maximum
References