Beat Wave Accelerator Research Articles

The detuning of relativistic Langmuir waves in the beat-wave accelerator

In the beat-wave accelerator, a large-amplitude Langmuir wave is produced by the beating of two laser beams whose frequencies differ by approximately the plasma frequency. The growth of this Langmuir wave saturates because of a nonlinear shift in its natural frequency. At present, there are three different formulas for the nonlinear frequency shift in the literature. By taking all relevant nonlinearities into account, the original result of Akhiezer and Polovin [Dokl. Akad. Nauk SSSR 102, 919 (1955)] is shown to be correct. The maximum amplitude of the Langmuir wave depends on the incident laser intensity and the frequency mismatch, which is the difference between the beat frequency of the incident waves and the plasma frequency. Two different studies have produced contradictory conclusions on the ‘‘optimum’’ frequency mismatch. The reasons for this contradiction are discussed and the result of Tang, Sprangle, and Sudan [Phys. Fluids 28, 1974 (1985)] is shown to be essentially correct. However, the requirements for effective beam loading make practical use of the optimum configuration impossible.

Beat-wave acceleration.

This report reviews the research on a new accelerator concept which uses an intense laser light, that is to say, the plasma beat-wave accelerator. Intense colinear laser beams ωo ko and ω1 k1 shone on a plasma with a frequency seperation equal to the electron plasma frequency ωP can creat a large coherent longitudinal electric field of a few tens GV/m by the laser beat excitation of plasma oscillations. Accompanying favourable and deleterious physical effects using this process for a high energy beatwave accelerator are discussed : dephasing, pump depletion, plasma turbulence effects, plasma fibre effects, surfatron, wakeless triple-soliton, etc.

Temporal Energy Cascading in the Beat Wave Accelerator

A preliminary analytic study of the temporal evolution of the beat wave accelerator (BWA) has been conducted. It was found that while energy cascading is crucial to the interpretation of current simulations, it will be less important in an actual device where the existing simple fluid model will be adequate.

A Microwave-Driven Beat Wave Accelerator for Scaled Experments

It is shown that large-amplitude (~ 104 V/cm) plasma waves can be resonantly excited by beating microwave pumps in an open resonator filled with plasma of subcritical density. The advantages and the possibilities of scaled experiments on beat wave accelerator concepts are discussed, in particular the plasma wave growth and saturation and the role of competing instabilities.

Laser accelerators (Recent topics on beat wave acceleration).

Recently, very high longitudinal acceleration field has been observed experimentally in a laser pro-duced plasmas which are irradiated by a two frequency laser light. This report reviews researches on new accelerator concepts which use an intense laser light. In particular, the difficulties associating with the laser beat wave acceleration are discussed to clarity the future prospects of the laser beat wave accelerator. Some new ideas which overcome the some of above difficulties are also presented.

Relativistic solitary-wave solutions of the beat-wave equations.

The relativistic equations governing the nonlinear interaction of two light waves and a Langmuir wave are shown to admit two classes of solitary-wave solutions. Temporal solitary waves propagate at speeds greater than the speed of light and carry no information. Spatial solitary waves propagate at speeds less than the speed of light and do carry information. The properties of these waves are discussed and the spatial solitary waves are shown to be well suited to the beat-wave acceleration of particles.

The quest for ultrahigh energies

A categorization is given of all the methods for accelerating particles. It is shown that in principle one can employ the large fields of a laser for this purpose as well as the wake fields of intense low-energy particle beams. Discussion is given of four acceleration schemes which offer the possibility of attaining very high-energy particles; namely, the inverse free-electron laser accelerator, the beat-wave accelerator, the wake-field accelerator, and the two-beam accelerator.

Generation of radial fields in the beat-wave accelerator for Gaussian pump profiles.

In a simple, linear fluid model we obtain the longitudinal and radial electric field components generated by the propagation of two electromagnetic waves resonantly beating in a plasma, assuming Gaussian profiles for the pump amplitudes.

Electromagnetic field cascading in the beat-wave generation of plasma waves.

A general analytical solution for the temporal (or spatial) evolution of electromagnetic cascading in the context of beat-wave generation of intense plasma waves is given. The amplitude of the nonlinear beat plasmon can be solved separately, after which the solution of the whole electromagnetic cascade can be constructed in terms of Bessel functions. Implications of the analytical model for the beat-wave acceleration, plasma heating, and laser fusion are discussed.

High energy laser plasma accelerators

Intense colinear laser beams ω0, k0 and ω1, k1, shone on a plasma with a frequency separation equal to the electron plasma frequency ωpe are capable of creating a large coherent longitudinal electric field EL = mcωpe/e of the order of 1 GeV/cm for a plasma density of 1018 cm-3 by the laser beat excitation of plasma oscillations. Accompanying favourable and deleterious physical effects using this process for a high energy beatwave accelerator are discussed: longitudinal dephasing, pump depletion, transverse laser diffraction, plasma turbulence effects, self-steepening, self-focusing, etc. The basic equation, the driven nonlinear Schrödinger equation, is derived to describe this system. Advanced accelerator concepts to overcome some of these problems are proposed, including various forms of the plasma fiber accelerator. An advanced laser architecture suitable for the beat-wave accelerator is suggested. Accelerator physics issues such as the luminosity are discussed. Applications of the present process to the current drive in a plasma and to the excitation of collective oscillations within nuclei are also discussed.

Pump Depletion and Laser Staging for Beat-Wave Accelerator

The beat-wave accelerator (BWA) scheme is promising for a large acceleration gradient for high energies. Some of the concerns with this accelerator concept are (i) the longitudinal dephasing between the speed of high energy particles and that of plasmons and (ii) the laser pump depletion. The latter problem is analyzed in detail here. To cope with these problems and also to ease some of the requirements on laser and plasma parameters, we propose an accelerator architecture for BWA with the following features: (i) distributed laser staging optically connected by the master oscillator; (ii) optical delay lines synchronizing the timing and phase of each laser stage; (iii) appropriate mirror systems; and (iv) optical guides (plasma fiber) to trap laser beams by acoustic transducers or other mechanism. If necessary, additional collector devices may be added to collect any unused portion of laser power and to convert it for reuse.

The "Phase Velocity" of Nonlinear Plasma Waves in the Laser Beat-Wave Accelerator

A calculational scheme for beat-wave accelerators is introduced that includes all orders in velocity and in plasma density, and additionally accounts for the influence of plasma nonlinearities on the wave's phase velocity. The main assumption is that the laser frequencies are very large compared to the plasma frequency - under which it is possible to sum up all orders of forward Raman scattering. It is found that the nonlinear plasma wave does not have simply a single phase velocity, but that the beat-wave which drives it is usefully described by a non-local ''effective phase velocity'' function. A time-space domain approach is followed. (LEW)

Study of the Plasma Fiber Accelerator

We study the plasma fiber accelerator concept by simulation and theory. An outgrowth of the laser beat-wave accelerator concept, the plasma fiber accelerator, sets the phase velocity of the beat plasma wave at the speed of light (or any value desired) by allowing each laser light to have a specific transverse wavenumber (or structure). Two-dimensional slab duct structures with laser beams of both transverse electric and transverse magnetic polarizations are explored. Accelerated beam dynamics in fiber beat-wave is discussed.

Beat-wave excitation of plasma waves

Nonlinear saturation effects associated with the generation of electron plasma waves by two high-frequency electromagnetic waves, beating at a frequency nearly equal to the electron plasma frequency, are studied. A fluid model including collisions, frequency mismatch and relativistic mass variation is used. It is shown that for large-amplitude driving waves a transition to chaos can occur, leading to plasma wave breakdown. The results may be relevant to the beat-wave current drive in tokamak devices and to beat-wave particle accelerators.

Plasma-wave generation in the beat-wave accelerator.

We analytically study the generation of longitudinal plasma waves in an underdense plasma by two electromagnetic waves with frequency difference approximately equal to the plasma frequency, as envisioned in the plasma beat-wave accelerator concept of Tajima and Dawson (Phys. Rev. Lett. 43, 267 (1979)). The relativistic electron fluid equations describing driven electron oscillations with phase velocities near the speed of light in a cold, collisionless plasma are reduced to a single, approximate ordinary differential equation of a parametrically excited nonlinear oscillator. We give amplitude-phase equations describing the asymptotic solutions to this equation valid for plasma-wave amplitudes below wave breaking. We numerically compare the behavior of the asymptotic equations with that of the original equation and with particle-simulation results.

Dynamics of space-charge waves in the laser beat wave accelerator

The excitation of plasma waves by two laser beams, whose frequency difference is approximately the plasma frequency, is analyzed. Our nonlinear analysis is fully relativistic in the axial and transverse directions and includes mismatching of the laser beat frequency to the plasma frequency, time dependent laser amplitudes, and an applied transverse magnetic field (surfatron configuration). Our analytical results for the large amplitude plasma waves include an axial constant of motion, accelerating electric field, and its phase velocity. The analytical results in the weak laser power limit are in good agreement with numerical results obtained from the complete equations. The imposed transverse magnetic field is found to increase the effective plasma frequency, but has little effect on the plasma dynamics.

Laser beat-wave accelerator and plasma noise.

Plasma noise effects on the beat-wave resonance condition and the subsequent reduction of the accelerating electric field for the laser beat-wave accelerator are investigated. Plasma noise or turbulence causes the accelerating electric field to saturate at a reduced level \ensuremath{\epsilon}=${L}_{\mathrm{eff}/\mathrm{L}}$ of the ideal coherent accelerating field, where ${L}_{\mathrm{eff}}$ is the effective growth length for the plasma wave and L is the ideal growth length. When the noise parameter \ensuremath{\sigma}=〈(\ensuremath{\delta}n${)}^{2}$〉/${n}^{2}$ is above a threshold value, we find ${L}_{\mathrm{eff}\mathrm{\ensuremath{\simeq}}2\mathrm{c}/{\ensuremath{\omega}}_{p}^{2}{\ensuremath{\tau}}_{c}\mathrm{\ensuremath{\sigma}}}$, where ${\ensuremath{\tau}}_{c}$ is the correlation time of the noise spectrum along \ensuremath{\omega}=${\mathrm{kv}}_{p}$. Slower noise is less effective in limiting the plasma wave growth. For strong noise ${L}_{\mathrm{eff}}$ becomes shortened to the correlation length in the noise ${L}_{c}$=${v}_{p}$${\ensuremath{\tau}}_{c}$. In the case of slowly increasing mismatch in the beat-wave resonance condition, the effective growth length ${L}_{\mathrm{eff}}$ becomes the geometric mean of the density gradient scale length ${L}_{n}$ and the collisionless skin depth (${L}_{n}$c/${\ensuremath{\omega}}_{p}$${)}^{1/2}$. .AE

Double Beat-Wave Particle Acceleration

Described are two mechanisms which make it possible for an accelerated charged particle to stay in phase indefinitely with a moving accelerating potential well set up by electromagnetic radiation in a plasma beat-wave accelerator. 1) Double beat-wave mechanism, in which interference between two beatwaves cancel a) the fields in the interfering electromagnetic waves, b) the electron oscillations which would otherwise be set up by those waves. 2) Alternating density mechanism, in which one or each of two beat-waves set up resonant electron oscillations in alternate plasma regions, but not in others.

Excitation of the plasma waves in the laser beat wave accelerator

The excitation of plasma waves by two laser beams, whose frequency difference is approximately the plasma frequency, is analyzed. Our nonlinear analysis is fully relativistic and includes mismatching of the laser beat frequency to the plasma frequency, time dependent laser amplitudes, and an applied transverse magnetic field (surfatron). For a given beat frequency, laser power, and plasma density, we find the peak accelerating electric field and its phase velocity. The transverse magnetic field is found to increase the effective plasma frequency, but has little effect on the plasma dynamics.

A Plasma Wave Accelerator - Surfatron II

Particles may be accelerated to arbitrarily high energy as they ride across the wave fronts. This paper describes this phenomenon for the Surfatron 1. The limitation on the total energy gain possible with recent plasma accelerator schemes such as the beat-wave accelerator of Tajima and Dawson is overcome by the Surfatron. By introducing a perpendicular magnetic field it is possible to keep particles in phase with the laser-induced plasma waves and hence accelerate them to arbitrarily high energy. The beat-wave accelerator is one scheme proposed by Dawson and Tajima to excite large amplitude electrostatic plasma waves which can accelerate particles. The authors have shown that classical particles trapped by a perpendicularly propagating electrostatic wave are accelerated until they de-trap near the E x B. (cE/B). In this paper it is considered that the relativistic effects introduced when the E x B velocity is greater than the speed of light and when the wave's phase velocity is not small compared to c. The authors treat the trapped particle motion analytically and numerically, followed by application of these results to the beat wave example. Considered is a plane wave electric field and uniform magnetic field.