Robust Autoresonant Excitation in the Plasma Beat-Wave Accelerator

Abstract

A modified version of the Plasma Beat-Wave Accelerator scheme is introduced and analyzed, which is based on autoresonant phase-locking of the nonlinear Langmuir wave to the slowly chirped beat frequency of the driving lasers via adiabatic passage through resonance. This new scheme is designed to overcome some of the well-known limitations of previous approaches, namely relativistic detuning and nonlinear modulation or other non-uniformity or non-stationarity in the driven Langmuir wave amplitude, and sensitivity to frequency mismatch due to measurement uncertainties and density fluctuations and inhomogeneities. As in previous schemes, modulational instabilities of the ionic background ultimately limit the useful interaction time, but nevertheless peak electric fields at or approaching the wave-breaking limit seem readily attainable. Compared to traditional approaches, the autoresonant scheme achieves larger accelerating electric fields for given laser intensity, or comparable fields for less laser power; the plasma wave excitation is much more robust to variations or uncertainties in plasma density; it is largely insensitive to the precise choice of chirp rate, provided only that chirping is sufficiently slow; and the quality and uniformity of the resulting plasma wave and its suitability for accelerator applications may be superior. In underdense plasmas, the total frequency shift required is only of the order of a few percent of the laser carrier frequency, and for possible experimental proofs-of-principle, the scheme might be implemented with relatively little additional modification to existing systems based on either solid-state amplifiers and Chirped Pulse Amplification techniques, or, with somewhat greater technological effort, using a CO2 or other gas laser system.

Complete pump depletion by autoresonant second harmonic generation in a nonuniform medium

“…The analytical solutions, Eqs. (19) and (20), are plotted in Figs. 1 and 2 and are found to be in excellent agreement with the local average of the numerical solution as long as phase-locking is preserved.…”

“…In (a), the fundamental wave B 1 and the second harmonic wave B 2 are plotted by red and blue, respectively, and the black curves represent the value of the analytical expressions Eqs. (19) and (20). The vertical dashed line is located at jαjξ 2 p where complete pump depletion is obtained and phaselocking is lost.…”

“…Utilizing autoresonance in wave-mixing processes allows to transfer energy between one type of wave or mode in the system to another with very high conversion efficiency. The attractive advantages of autoresonant wave mixing have already been demonstrated in additional processes to those mentioned above, e.g., two-wave interaction in nonlinear optics [16,17] and stimulated Raman scattering in plasmas [18][19][20][21][22][23].…”

DC-like Phase Space Manipulation and Particle Acceleration Using Chirped AC Fields

“…There are of course many specific wave mechanisms that have been advanced, such as recently: ponderomotive accelerations where particles exit a ponderomotive potential in an appropriate way [11][12][13][14][15][16][17][18][19][20][21][22][23]; ratchet effects using a cyclotron resonance [24][25][26]; and wakefield acceleration effects [27] including acceleration in plasma channels [28].…”

Direct-current-like phase space manipulation using chirped alternating current fields

“…1,2 The idea of producing holes in phase space through BGK modes has been explored further both experimentally and theoretically. [6][7][8] There are of course in addition many specific wave mechanisms that have been advanced to manipulate a particle distribution in phase space, such as recently ponderomotive methods where particles exit a ponderomotive potential in an appropriate way, [9][10][11][12][13][14][15][16][17][18][19][20] ratchet effects using a cyclotron resonance, [21][22][23] and wakefield acceleration effects 24 including acceleration in plasma channels. 25 The particle dynamics underlying all of these applications is by now well researched.…”