Electron kinetic effects in plasma expansion and ion acceleration

Expansion of a collisionless hypersonic plasma plume into a vacuum

Both fully kinetic and hybrid particle-in-cell (PIC) simulations are performed to investigate the two-dimensional (2D) expansion of a collisionless, hypersonic plasma plume into a vacuum. The fully kinetic PIC simulations are carried out using the real ion-to-electron mass ratios of H^{+}, Ar^{+}, and Xe^{+}, while the hybrid PIC model assumes the electrons to be a massless, isothermal fluid. We find that the hypersonic plasma plume exhibits four distinct regions, the unperturbed, quasisteady expansion, self-similar expansion and electron front regions. The behavior of electrons is strongly anisotropic, causing considerably different expansion characteristics between the plume direction and the transverse direction. Along the plume direction, the expansion dynamics is similar to that of the classical one-dimensional (1D) semi-infinite plasma expansion and the electrons are almost isothermal. In the transverse direction, the expansion process can be considered analogous to the 1D expansion of a finite plasma where the effect of electron cooling is important. This anisotropic characteristic is attributed to the amount of electron thermal energy available from the source in different directions. A direct comparison between the hybrid and full PIC simulations shows that the widely used equilibrium isothermal electron fluid model is in general not valid for modeling the expansion of a collisionless plasma plume.

Multispecies plasma expansion into vacuum: The role of secondary ions and suprathermal electrons

The self-similar expansion of multispecies ion plasma is investigated by a two-ion fluid model with adiabatic equation of state for each ionic species. Our aim is to elucidate the effect of secondary ions on a plasma expansion front, in combination with energetic (suprathermal) electrons in the background, modeled by a kappa-type distribution function. The plasma density, velocity, and electric-field profile is investigated. It is shown that energetic electrons have a significant effect on the expansion front dynamics, essentially energizing the front, thus enhancing the ion acceleration mechanism. Different special cases are considered as regards the relative magnitude of the ion mass and/or charge state.

Ion cooling in collisionless plasma expansion

The ion cooling in collisionless plasma expansion is revisited. It is shown that, in the case of an initial Maxwellian ion distribution, the ion cooling is much slower than predicted by an adiabatic law linking the ion temperature to the ion density. The origin of this behavior is a strong distortion of the ion distribution function resulting in a large ion heat flow (not predicted by a simple water-bag model). Also noticeable is the increase of the electron heat flux in the unperturbed plasma compared to the zero ion temperature case.

Plasma expansion into vacuum assuming a steplike electron energy distribution

The expansion of a semi-infinite plasma slab into vacuum is analyzed with a hydrodynamic model implying a steplike electron energy distribution function. Analytic expressions for the maximum ion energy and the related ion distribution function are derived and compared with one-dimensional numerical simulations. The choice of the specific non-Maxwellian initial electron energy distribution automatically ensures the conservation of the total energy of the system. The estimated ion energies may differ by an order of magnitude from the values obtained with an adiabatic expansion model supposing a Maxwellian electron distribution. Furthermore, good agreement with data from experiments using laser pulses of ultrashort durations τ(L)</~80fs is found, while this is not the case when a hot Maxwellian electron distribution is assumed.

Thin-foil expansion into a vacuum with a two-temperature electron distribution function

A kinetic theory of the expansion into a vacuum of a plasma thin foil with initially a hot and a cold Maxwellian electron population is examined with a one-dimensional kinetic code. Whereas hot electrons always lose energy to expanding ions, cold electrons can either gain or lose energy depending on the initial temperature and density ratios and on time. When the cold electrons' density is not too large, they experience initially an adiabatic compression by the electric field associated with the rarefaction wave. The corresponding temperature increase can be as large as a factor of a few tens. Later on, as expected, the cold electrons eventually lose energy to the expansion. When cold electrons are numerically dominant, a rarefaction shock appears during the first phase of the expansion. Hot electrons cool down faster than cold electrons, thus reducing the effective temperature ratio. Furthermore, the amplitude of the rarefaction shock and the dip that it causes on the ion velocity spectrum tend to be smoothed out by the expansion.

Rarefaction shock in plasma with a bi-Maxwellian electron distribution function

The one-dimensional collisionless expansion into a vacuum of a plasma with a bi-Maxwellian electron distribution function and a single ion species is studied both theoretically and numerically. A shock wave occurs when the ratio of the temperatures between the hot and the cold electrons is larger than 5+√24 [B. Bezzerides, D. W. Forslund, and E. L. Lindman, Phys. Fluids 21, 2179 (1978)]. The theoretical model presented here gives a coherent and complete description of the rarefaction shock and its effects on the ion acceleration process. Analytical expressions of the characteristics of the shock are given. The analytical findings are compared to the results of a hybrid code describing the plasma expansion, and an excellent agreement is obtained.

Time and space resolved interferometry for laser-generated fast electron measurements

A technique developed to measure in time and space the dynamics of the electron populations resulting from the irradiation of thin solids by ultraintense lasers is presented. It is a phase reflectometry technique that uses an optical probe beam reflecting off the target rear surface. The phase of the probe beam is sensitive to both laser-produced fast electrons of low-density streaming into vacuum and warm solid density electrons that are heated by the fast electrons. A time and space resolved interferometer allows to recover the phase of the probe beam sampling the target. The entire diagnostic is computationally modeled by calculating the probe beam phase when propagating through plasma density profiles originating from numerical calculations of plasma expansion. Matching the modeling to the experimental measurements allows retrieving the initial electron density and temperature of both populations locally at the target surface with very high temporal and spatial resolution (~4 ps, 6 μm). Limitations and approximations of the diagnostic are discussed and analyzed.

Influence of the Weibel instability on the expansion of a plasma slab into a vacuum

The development of the Weibel instability during the expansion of a thin plasma foil heated by an intense laser pulse is investigated, using both analytical models and relativistic particle-in-cell simulations. When the plasma has initially an anisotropic electron distribution, this electromagnetic instability develops from the beginning of the expansion. Then it contributes to suppress the anisotropy and eventually saturates. After the saturation, the strength of the magnetic field decreases because of the plasma expansion until it becomes too weak to maintain the distribution isotropic. For this time, the anisotropy rises as electrons give progressively their longitudinal energy to ions, so that a new instability can develop.

Self-generation of megagauss magnetic fields during the expansion of a plasma

The expansion of a plasma slab into a vacuum is studied using one-dimensional and two-dimensional particle-in-cell simulations. As electrons transfer their longitudinal kinetic energy to ions during the expansion, the electron temperature becomes anisotropic. Once this anisotropy exceeds a threshold value, it drives the Weibel instability, leading to magnetic fields in the megagauss range. These fields induce energy transfer between the longitudinal and transverses directions, which influences the expansion. The impact of a cold electron population on this phenomenon is also investigated.

Rarefaction acceleration and kinetic effects in thin-foil expansion into a vacuum

The collisionless expansion into a vacuum of a thin plasma foil adiabatically cooling down is studied with a particular emphasis on the evolution of the electron distribution function. It is shown that during the expansion the bulk of the distribution function evolves towards a top-hat distribution. As a result, while the electrons globally lose energy in favor of the ions, the rarefaction wave accelerates until it reaches the center of the foil. The electron temperature becomes strongly inhomogeneous, with a maximum in the center of the foil, a strong dip in the outer part of the foil, and a constancy of the initial temperature in the far corona.