arXiv subjects
Publications and source records attributed to N. J. Fisch.
Charged particles can be accelerated via surfatron mechanism along dc magnetic field by obliquely propagating electrostatic waves. In plasma, this mechanism can, in principle, produce an average parallel current, even when the wave frequency is much larger than the gyrofrequency and the wave phase velocity is much larger than particle initial velocities.
A Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic time-averaged Lagrangian density $\mcc{L}$ is expressed in terms of the single-particle oscillation-center Hamiltonians; once those are found, the complete set of geometrical-optics equations is derived without referring to the Maxwell-Vlasov system. The number of trapped particles is assumed fixed; in particular, those may reside close to the bottom of the wave trapping potential, so they never become untrapped. Then their contributions to the wave momentum and the energy flux depend mainly on the trapped-particle density, as an independent parameter, and the phase velocity rather than on the wave amplitude $a$ explicitly; hence, $\mcc{L}$ acquires $a$-independent terms. Also, the wave action is generally not conserved, because it can be exchanged with resonant oscillations of the trapped-particle density. The corresponding modification of the wave envelope equation is found explicitly, and the new action flow velocity is derived. Applications of these results are left to the other two papers of the series, where specific problems are addressed pertaining to properties and dynamics of waves with trapped particles.
A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift $ω_{\rm NL}$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $ω_{\rm NL} \propto \sqrt{a}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic $ω_{\rm NL}(a)$ is generally nonlocal.
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter $S$, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At $S < 1/2$, a wave is stable and exhibits group velocity splitting. At $S > 1/2$, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schrödinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.
This study concerns a situation when measurements of the nonresonant cross-section of nuclear reactions appear highly dependent on the environment in which the particles interact. An appealing example discussed in the paper is the interaction of a deuteron beam with a target of deuterated metal Ta. In these experiments, the reaction cross section for d(d,p)t was shown to be orders of magnitude greater than what the conventional model predicts for the low-energy particles. In this paper we take into account the influence of quantum effects due to the Heisenberg uncertainty principle for particles in a non-ideal medium elastically interacting with the medium particles. In order to calculate the nuclear reaction rate in the non-ideal environment we apply both the Monte Carlo technique and approximate analytical calculation of the Feynman diagram using nonrelativistic kinetic Green's functions in the medium which correspond to the generalized energy and momentum distribution functions of interacting particles. We show a possibility to reduce the 12-fold integral corresponding to this diagram to a fivefold integral. This can significantly speed up the computation and control accuracy. Our calculations show that quantum effects significantly influence reaction rates such as p +7Be, 3He +4He, p +7Li, and 12C +12C. The new reaction rates may be much higher than the classical ones for the interior of the Sun and supernova stars. The possibility to observe the theoretical predictions under laboratory conditions is discussed.
A new amplification method, weaving the three basic compression techniques, Chirped Pulse Amplification (CPA), Optical Parametric Chirped Pulse Amplification (OPCPA) and Plasma Compression by Backward Raman Amplification (BRA) in plasma, is proposed. It is called C3 for Cascaded Conversion Compression. It has the capability to compress with good efficiency kilojoule to megajoule, nanosecond laser pulses into femtosecond pulses, to produce exawatt and beyond peak power. In the future, C3 could be used at large-scale facilities such as the National Ignition Facility (NIF) or the Laser Megajoule (LMJ) and open the way to zettawatt level pulses. The beam will be focused to a wavelength spot size with a f#1. The very small beam size, i.e. few centimeters, along with the low laser repetition rate laser system will make possible the use of inexpensive, precision, disposable optics. The resulting intensity will approach the Schwinger value, thus opening up new possibilities in fundamental physics.
A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential form from a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift $Δω$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $Δω\sim a^{1/2}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation.
The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The equation accounts simultaneously for the Lorentz force and the effects of general relativity, with the latter appearing as the gravity force and an additional force due to the extrinsic curvature of spatial hypersurfaces. For an arbitrary spatial metric, the equations of collisionless hydrodynamics are also obtained in the usual three-vector form.
Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry.
The oscillation-center Hamiltonian is derived for a relativistic electron injected with an arbitrary momentum in a linearly polarized laser pulse propagating in tenuous plasma, assuming that the pulse length is smaller than the plasma wavelength. For hot electrons generated at collisions with ions under intense laser drive, multiple regimes of ponderomotive acceleration are identified and the laser dispersion is shown to affect the process at plasma densities down to 10^17 cm-3. Assuming a/gamma_g << 1, which prevents net acceleration of the cold plasma, it is also shown that the normalized energy gamma of hot electrons accelerated from the initial energy gamma_0 <~ Gamma does not exceed Gamma ~ a gamma_g, where a is the normalized laser field, and gamma_g is the group velocity Lorentz factor. Yet gamma ~ Gamma is attained within a wide range of initial conditions; hence a cutoff in the hot electron distribution is predicted.
For a nonrelativistic classical particle undergoing arbitrary oscillations, the generalized effective potential Y is derived from nonlinear eigenfrequencies of the particle-field system. Specifically, the ponderomotive potential is extended to a nonlinear oscillator, resulting in multiple branches near the primary resonance. For a pair of natural frequencies in a beat resonance, Y scales linearly with the internal actions and is analogous to the dipole potential for a two-level quantum system. Thus cold quantum particles and highly-excited quasiclassical objects permit uniform manipulation tools, particularly, one-way walls.
A classical particle oscillating in an arbitrary high-frequency or static field effectively exhibits a modified rest mass m_eff derived from the particle averaged Lagrangian. Relativistic ponderomotive and diamagnetic forces, as well as magnetic drifts, are obtained from the m_eff dependence on the guiding center location and velocity. The effective mass is not necessarily positive and can result in backward acceleration when an additional perturbation force is applied. As an example, adiabatic dynamics with m_|| > 0 and m_|| < 0 is demonstrated for a wave-driven particle along a dc magnetic field, m_|| being the effective longitudinal mass derived from m_eff. Multiple energy states are realized in this case, yielding up to three branches of m_|| for a given magnetic moment and parallel velocity.
The formation of plasma channels with nonuniformity of about +- 3.5% has been demonstrated. The channels had a density of 1.2x10^19 cm-3 with a radius of 15 um and with length >= 2.5 mm. The channels were formed by 0.3 J, 100 ps laser pulses in a nonflowing gas, contained in a cylindrical chamber. The laser beam passed through the chamber along its axis via pinholes in the chamber walls. A plasma channel with an electron density on the order of 10^18 - 10^19 cm-3 was formed in pure He, N2, Ar, and Xe. A uniform channel forms at proper time delays and in optimal pressure ranges, which depend on the sort of gas. The influence of the interaction of the laser beam with the gas leaking out of the chamber through the pinholes was found insignificant. However, the formation of an ablative plasma on the walls of the pinholes by the wings of the radial profile of the laser beam plays an important role in the plasma channel formation and its uniformity. A low current glow discharge initiated in the chamber slightly improves the uniformity of the plasma channel, while a high current arc discharge leads to the formation of overdense plasma near the front pinhole and further refraction of the laser beam. The obtained results show the feasibility of creating uniform plasma channels in non-flowing gas targets.
We show how to construct asymmetric optical barriers for atoms. These barriers can be used to compress phase space of a sample by creating a confined region in space where atoms can accumulate with heating at the single photon recoil level. We illustrate our method with a simple two-level model and then show how it can be applied to more realistic multi-level atoms.
A diagnostic setup for characterization of near-anode processes in Hall-current plasma thrusters consisting of biased and emissive electrostatic probes, high-precision positioning system and low-noise electronic circuitry was developed and tested. Experimental results show that radial probe insertion does not cause perturbations to the discharge and therefore can be used for accurate near-anode measurements.
An interesting phenomenon observed in the near-anode region of a Hall thruster is that the anode fall changes from positive to negative upon removal of the dielectric coating, which is produced on the anode surface during the normal course of Hall thruster operation. The anode fall might affect the thruster lifetime and acceleration efficiency. The effect of the anode coating on the anode fall is studied experimentally using both biased and emissive probes. Measurements of discharge current oscillations indicate that thruster operation is more stable with the coated anode.
The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of a slightly inhomogeneous intense laser field are obtained. In weak low-frequency background fields, such a particle on average drifts with an effective, relativistically invariant mass, which depends on the laser intensity. The essence of the proposed ponderomotive formulation is presented in a physically intuitive and mathematically simple form, yet represents a powerful tool for studying various nonlinear phenomena caused by interaction of currently available smooth ultra-intense laser pulses with plasmas.
A method of determining boundary conditions for quasi 1-D modeling of steady-state operation of a Hall Thruster with ceramic channel is presented. For a given mass flow rate and magnetic field profile the imposed condition of a smooth sonic transition uniquely determines plasma density at the anode. The discharge voltage determines the structure of the anode sheath and thus determines electron and ion velocities at the anode. These parameters appear to be sufficient for constructing a solution with given temperature profile. It is shown that a good correlation between simulated and experimental results can be achieved by selecting an appropriate electron mobility and temperature profile. The structure of the electrode sheath was studied theoretically over a wide range of input parameters, such as discharge voltage, incoming neutral velocity and channel length, and the possibility of realization of the no-sheath operating regime is discussed here.