I.V. Pogorelsky

Abstract. The first terawatt picosecond (TWps) CO₂ laser is under construction at the BNL Accelerator Test Facility (ATF). TWps-CO₂ lasers, having an order of magnitude longer wavelength than solid state lasers, offer new opportunities for strong-field physics research. For laser wakefield accelerators (LWFA) the advantage of the new class of lasers is due to a gain of two orders of magnitude in the ponderomotive potential. The demonstrated large average power of CO₂ lasers is important for the generation of hard radiation through Compton back-scattering of the laser off energetic electron beams. We discuss applications of TWps-CO₂ lasers for LWFA modules of a tentative electron-positron collider, for a g -g (or g -lepton) collider, for a possible "table-top" source of high-intensity x-rays and gamma rays, and the generation of polarized positron beams.

 

Terawatt picosecond lasers are known as the sources of the most intense electromagnetic radiation and strongest electric and magnetic fields available for laboratory research. Their development stimulated a number of strong-field physics disciplines to emerge during the last decade. One of such applications is laser-driven high-gradient particle accelerators. According to equation

(1)

or , (1a)

where E_L , I_L, P_L, r_L are correspondingly the laser electric field, intensity, power, and focal spot radius, focusing of a terawatt laser beam to r_L=10 m m results in an intensity of I_L » 10¹⁸ W/cm² and, associated with it, an electric field of E_L» 1 TV/m. This exceeds by four orders of magnitude accelerating fields available in conventional particle accelerators. Various methods to convert at least a portion of such an enormous transverse fast-oscillating field into a longitudinal accelerating electric field have been proposed. Using the LWFA technique [1,2], about 30 GeV/m electron acceleration gradients have been demonstrated [3,4]. In these experiments solid state terawatt lasers based on mode-locked picosecond pulse generation and pulse chirped amplification [5] and operating at wavelength near l » 1 m m have been utilized.

Emerging TWps-CO₂ lasers having wavelength l » 10 m m may provide an additional boost to laser accelerator development towards practical devices. For the most part, this is based on the fact that the energy of oscillatory motion acquired by the electron from an electromagnetic wave, called ponderomotive potential

(2)

(where e and m are correspondingly the electron charge and mass and w is the laser frequency ) is quadratically proportional to l . Thus, any process, where the field-induced electron oscillation is paramount, is dramatically enhanced. The examples of such processes are: avalanche and tunneling ionization, plasma wave ponderomotive excitation, and relativistic self-focusing, which are especially relevant for electron acceleration in plasma, such as in the LWFA method.

The same physical effect is responsible for the l -proportional increase in Compton scattering cross-section thus opening additional prospects for relatively compact high-brightness x-ray and gamma sources [6].

The approach to utilize the long-wavelength laser radiation for particle acceleration and x-ray generation is pursued at the Brookhaven Accelerator Test Facility (ATF) where the first TWps-CO₂ laser is under construction [7].

In the present paper we review the opportunities provided by TWps-CO₂ laser technology for high-energy physics. This includes novel compact particle accelerators and monochromatic x-ray sources and prospects for their future development towards the electron-positron (e^--e⁺) and gamma (g ) colliders of the TeV energy range.

An important physical parameter that enables generation and amplification of picosecond laser pulses is the gain spectral bandwidth. In solid state lasers, radiation transitions in outer electron shells of active ions are broadened to 5-50 THz due to the perturbative action by the host matrix. Such a broad gain spectrum makes possible the generation and amplification of picosecond, and even femtosecond, laser pulses by the mode locking technique. Unlike the solid state, the spectral gain in the molecular gas discharge is periodically modulated by the rotational structure. Due to the discrete spectrum, and for other physical and technical reasons, mode-locking techniques do not work for CO₂ lasers as well as for solid state lasers.

However, alternative methods to produce picosecond and sub-picosecond CO₂ laser pulses have been developed. One of them is semiconductor optical switching [8]. Using this method, subpicosecond slices out of a multi-nanosecond CO₂ laser output may be produced using a conventional mode-locked solid-state laser.

Pressure broadening of the CO₂ gain spectrum at ~10 atm into a 1 THz wide quasi-continuum permits direct amplification of multi-terawatt l =10 m m laser beams.

For a t _L=1 ps pulse propagating in a 10-atm amplifier, the estimated small-signal gain is 3-4%/cm and the extractable specific energy is ~20 mJ/cm³. Taking into account that the total discharge volume may exceed 10 l, the possibility of extraction of as high as 100 J of energy in a picosecond pulse from a reasonably compact CO₂ laser amplifier looks realistic. However, the limiting factor to high energy extraction may be the damage threshold of the output window that is at the level of 0.5 J/cm². For an optical window of the ~100 cm² size, the extractable energy is 30-50 J which still permits ~30 TW peak power at a 1-ps laser pulse duration.

Thus, to attain terawatt peak power, a ~10-atm, ~10-l CO₂ amplifier is required. To maintain a uniform discharge under such conditions, the following requirements should be satisfied: a) strong penetrating preionization, b) ~1 MV voltage applied to the discharge, and c) the energy load of several kilojoules deposited in a relatively short, £ 300 ns, time interval. The first laser with such parameters is under construction at the ATF.

The ATF laser is intended as a test bench for proof-of principle evaluation of TWps-CO₂ technology for such strong-field physics applications as high-gradient laser accelerators and high-intensity Compton x-ray sources. For these purposes, the ATF also provides a high-brightness 50-MeV electron beam from a photocathode RF linac synchronized within subpicoseconds to the CO₂ laser pulse.

Fig.1 shows the principal optical diagram of the ATF TWps CO₂ laser system. The 1 MW, 100 ns pulse produced by a 1-atm CO₂ laser oscillator is sliced at a semiconductor switch controlled by the picosecond Nd:YAG laser. The high power will be attained via regenerative amplification and four additional passes through the preamplifier followed by three passes in the 10-atm, 10-l final amplifier with the beam expansion to its full 10-cm aperture.

Progress in the exploration of particle interactions relies upon the development of a new-generation of accelerators on a TeV energy scale. One of the prospective approaches is a linear e^--e⁺ collider based on high-gradient laser acceleration.

Among the known laser acceleration techniques, the LWFA [1] is considered as the most reliable approach. The LWFA method is based on the ponderomotive charge separation and a relativistic wake formation when a short laser pulse propagates in underdense plasma. The amplitude of the accelerating field, E_a, due to the charge separation in a plasma wave is

, (3)

where n_e is electron density in plasma, and a is the dimensionless laser vector-potential

The 50 TW peak laser power foreseeable with state-of-the art laser technology, and the laser pulse duration - close to the experimentally demonstrated minimum.

The plasma channels are filled with 100% ionized hydrogen gas at the density equal to . Normalized emittance of the particle beam calculated using the Highland formula [9] for gas scattering is

. (6)

Plasma channel length for every accelerator stage is ~30z₀, where z₀=p r_L²/l is the Rayleigh length. A 20 cm long evacuated dead space is assumed between the accelerating channels. Note that optics of the same focal length are used for both lasers.

The maximum number of particles per bunch is calculated by the condition that space charge field of the electron bunch does not effect the wakefield structure:.

We see that both design approaches illustrated in Table 1 demonstrate the LWFA capabilities to attain the desired 2.5 TeV electron energy in a compact multi-stage accelerator. However, the calculated requirements of the laser driver for two cases are essentially different.

With the 1-m m laser, the short t _L results in a proportionally small l p and N_e. Then, in order to satisfy the high luminosity requirements, the laser repetititon rate and, hence, the average output power should increase quadratically. This becomes orders of magnitude beyond any reasonable expectation for picosecond solid state laser technology and does not fit into the anticipated wall-plug power limits.

Table 1. Prospective Comparative Characteristics for Standard LWFA

Driven with 1-m m and 10-m m Lasers

Another potential advantage of using a longer period plasma wave is the ease in producing the seed electron bunch which is short enough to fit into the small portion of the wake period thus ensuring the good beam quality (small energy spread and emittance). For example, at t _L=1 ps and the resonance plasma wavelength l _p=600 m m the desirable electron bunch duration is t _b£ 200 fs. Contemporary photocathode RF guns tend to approach these requirements. In particular t _b=370 fs electron bunches of 2.5´ 10⁸ electrons, 0.15%, and e _n=0.5 mm.mrad have been demonstrated with the ATF photocathode RF gun [10].

The above comparative analysis of two alternative approaches to the 2.5 TeV collider serves to illustrate the problems related to laser wavelength scaling and should not be considered as the collider design proposal. For example, we did not address such important aspects as stage coupling, other sources of the emittance degradation, etc. Still, we believe that the presented approach may be helpful in designing the criteria for choosing the appropriate laser driver for compact GeV accelerators and for future linear colliders.

Synchrotrons equipped with wiggler magnets are the sources of x-ray fluxes at the level of 10¹⁸ photon/sec. According to another approach to a relatively compact high-brightness x-ray generator called laser synchrotron source (LSS), the laser beam acts on relativistic electrons as an electromagnetic wiggler with a period 10⁴-10⁵ times shorter than the magnetic undulator. Thus, LSS permits significant downsizing of the electron accelerator, or produces proportionally heavier photons than a conventional synchrotron source operating at the same e-beam energy.

A combination of a high-gradient LWFA with LSS may open a route to table-top wakefield LSS operating in x-ray and gamma regions. Proof-of-principle table-top LSS may be realized at the ATF using the 5-TW CO₂ laser and a 5 MeV photocathode electron gun. As shown in Fig.2 the CO₂ laser beam is split into two beams which are focused by parabolic mirrors at the entrance and exit of a plasma channel to drive both LWFA and LSS.

PIC simulations predict 250 MeV acceleration when a 4 TW CO₂ laser beam is focused into the waveguide with parameters shown in Table 2 [11]. At the exit of the waveguide, electrons accelerated in the plasma wake field interact with the second CO₂ laser beam, generating x-ray fluxes which can be orders of magnitude above numbers obtained with conventional synchrotron light sources.

Table 2. Design Parameters for Table-Top LSS

By Compton backscattering of the laser photons from the TeV electron beam, a high brightness TeV photon beam can be created. It opens an additional opportunity to study a variety of interaction processes by colliding e^-, e⁺ and g beams in any combination and at independently controlled polarizations.

The expression for the maximum gamma photon energy for linear (single photon) Compton backscattering is

, (7)

where E _e is the electron energy, and . At x>>1, the Compton photon energy approaches the electron energy, » E _e. For CO₂ laser, x=1 at E _e=0.5 TeV. Thus, the long wavelength of the CO₂ laser used for the e± Þ g converter at E _e=2.5 TeV does not significantly degrade w g .

Another strong requirement to the laser wavelength is set by rescattering of gamma photons on the laser beam into pairs through the reaction g +l Þ e^-+e⁺. This occurs when w w g >m²c⁴/. Based on this condition and using Eq.(7), the optimum laser wavelength is derived:

l [m m]=4.2E _e[TeV]. (8)

Then, for the 2.5 TeV collider the laser with l =10.5 m m is the optimum choice.

For t _L=1 ps, the probability of e± Þ g conversion,

/t _Lc², (9)

where s _C=1.9´ 10^-25 cm² is the Compton scattering cross-section, reaches unity at the laser pulse energy » 1 J.

The laser pulse repetition rate should match that of the e^--e⁺ collider. The TWps-CO₂ laser technology is envisioned to provide the laser source delivering picosecond pulses of a 1 J energy at several kW of average power to satisfy the requirements of the g -g collider. Relatively compact ~10 l discharge, high-pressure, fast-flow CO₂ lasers operating at a ~100 Hz repetition rate may serve this purpose when the energy stored in the laser medium is extracted by a train of a hundred pulses of a 1 ps length each following at a ~1 ns period. Such a regime looks not just feasible but also quite efficient, permitting extraction of a good portion of the stored CO₂ laser energy. Overall electric efficiency of the laser may approach 10%.

Lasers may be used also in polarized positron sources for e^--e⁺ colliders. Here, the backward Compton scattering serves as an intermediate process followed by pair production on a target or via two-photon rescattering. Polarization of the produced particles is controlled by the input laser beam. Capable of high average power and delivering ten times more photons than solid state lasers of the similar energy, picosecond CO₂ lasers become the optimum choice for this application as well. The projected positron source for the Japan Future Collider [12] employs a hundred of 1.5 kW CO₂ lasers of 150 Hz repetition rate and 50 ps pulse duration. This project appears likely to become the biggest utilization of CO₂ lasers in fundamental science.

The author wishes to thank I. Ben-Zvi and T. Tajima for helpful discussions.

The work is supported by the US Department of Energy.

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