The wave isWaveplasma waves one of the fundamental phenomena occurring in physics. Locally acting forces produce perturbations that propagate in space and time. Their dynamics shows features that allow general classifications of a wide variety of phenomena and, in the linear regime, general relations among the dynamic variables can be formulated.

Interaction of electronsTransport with ions and neutrals and their mutual interactions is at the basis of all kinds of kinetic transport in plasma: collisional absorption, heat conduction, viscosity, friction. It depends on the kind of transport which interactions dominate; in collisional absorption it is the electron-ion collisions. Heat conduction is determined by electron-electron and electron-ion encounters. Viscosity of the plasma is governed by ion-ion interaction, as the derivation of Navier-Stokes equation of Chap. 3 lets suggest. In the dilute neutral gas binary collisions dominate. Thereby the meaning of a collision is that the mutual interaction of two particles is short compared with the time that elapses up to the next close encounter of two partners and the laser period $$ T = 2\pi /\omega $$ .

Richness of instabilities is one of continuous surprises of plasmas. Instabilities confer an originally uniform plasma unexpected structures: density and temperature modulations; turbulent shocks, violent bursts, and extremely energetic jets in cosmic plasmas; islands, disruptions, and anomalous transport in magnetic and inertial fusion devices; down and up conversion of modes, fast particle jets, Terahertz and hard X-ray photons in laser plasmas. The characteristic unstable equilibrium scenario is this: an arbitrarily small perturbation of the equilibrium produces a force that grows proportional to the perturbation. The growth is always accompanied by an increase of kinetic energy of the system.

HotRadiationhot matter matter radiates. Low density plasmas also emit radiation in form of spectral lines and inverse continuum bremsstrahlung radiation to a low level. With increasing density and nuclear charge Z production of photons greatly intensifies and is emitted as black body radiation or evolves towards such by multiple interaction with cold dense matter. Its transport and evolution towards a Planckian spectrum is governed by the photon mean free path between two “collisions”.

Laser-matter interaction is a many body problem. In the classical realm already the three body problem is not solvable analytically. On the other hand understanding physics evolves along the analytic path. So, what is the solution to the dilemma? There is a twofold approach: development of collective concepts and models that are able to describe macroscopic aspects of matter, for example the many body phenomenon, to be summarized under the general concept of screening, with Debye screening as a special example.

In many respects the plasma may be considered as a medium that assumes any form provided by external boundaries and forces acting on it from outside. The main parameters are a local particle density $$n(\mathbf {x}, t)$$ , mass density $$\rho (\mathbf {x},t)$$ , flow velocity $$\mathbf {u}(\mathbf {x}, t)$$ , and internal energy density $$\epsilon _\mathrm{in}(\mathbf {x}, t)$$ . Microscopic order like crystalline structure or ordered micropatterns are of no interest. Such a medium is called a fluidFluid. Examples of fluids are water, magma, sand, air, ideal gas, but also steel under high pressure in the form press, a neutron star, and the plasma. Steel and sand are incompressibleFluidincompressible under technical pressures. At sufficiently high pressure and strain all fluids turn into compressible media.

The model of matter as a fluid provided us with conservation laws of mass, momentum, and energy. They hold for all kinds of fluids independently of their shape, their density, and their chemical composition. We have applied them successfully to describe neutral fluids like water or dilute gases, or plasma. The constituents of the plasma are electrically charged and couple strongly to electric fields and are, as a consequence, largely dominated by collective effects. For such phenomena modelling the plasma as a fluid turns out to be very appropriate.

Laser-driven collisonless electrostatic shock formation and the subsequent ion acceleration have been studied in near critical density plasmas. Particle-in-cell simulations show that both the speed of laser-driven collisionless electrostatic shock and the energies of shock-accelerated ions can be greatly enhanced due to fast laser propagation in near critical density plasmas. However, a response time longer than tens of laser wave cycles is required before the shock formation in a near critical density plasma, in contrast to the quick shock formation in a highly overdense target. More important, we find that some ions can be reflected by the collisionless shock even if the electrostatic potential jump across the shock is smaller than the ion kinetic energy in the shock frame, which seems against the conventional ion-reflection condition. These anomalous ion reflections are attributed to the strongly time-oscillating electric field accompanying laser-driven collisionless shock in a near critical density plasma.

The capability of ion acceleration with high power, pulsed lasers has become an active field of research in the past years. In this context, the radiation pressure acceleration (RPA) mechanism has been the topic of numerous theoretical and experimental publications. Within that mechanism, a high power, pulsed laser beam hits a thin film target. In contrast to the target normal sheath acceleration, the entire film target is accelerated as a bulk by the radiation pressure of the laser. Simulations predict heavy ion beams with kinetic energy up to GeV, as well as solid body densities. However, there are several effects which limit the efficiency of the RPA: On the one hand, the Rayleigh-Taylor-instability limits the predicted density. On the other hand, conventional accelerator elements, such as magnetic focusing devices are too bulky to be installed right after the target. Therefore, we present a new beam transport method, suitable for RPA-like/over-dense plasma beams: laser induced focusing.

Among the various attempts to understand collisionless absorption of intense and superintense ultrashort laser pulses, a whole variety of models and hypotheses has been invented to describe the laser beam target interaction. In terms of basic physics, collisionless absorption is understood now as the interplay of the oscillating laser field with the space charge field produced by it in the plasma. A first approach to this idea is realized in Brunel's model the essence of which consists in the formation of an oscillating charge cloud in the vacuum in front of the target, therefore frequently addressed by the vague term "vacuum heating." The investigation of statistical ensembles of orbits shows that the absorption process is localized at the ion-vacuum interface and in the skin layer: Single electrons enter into resonance with the laser field thereby undergoing a phase shift which causes orbit crossing and braking of Brunel's laminar flow. This anharmonic resonance acts like an attractor for the electrons and leads to the formation of a Maxwellian tail in the electron energy spectrum. Most remarkable results of our investigations are the Brunel like spectral hot electron distribution at the relativistic threshold, the minimum of absorption at I lambda(2) congruent to (0.3 - 1.2) x 10(21) Wcm(-2) mu m(2) in the plasma target with the electron density of ne lambda(2) similar to 10(23) cm(-3) mu m(2), the drastic reduction of the number of hot electrons in this domain and their reappearance in the highly relativistic domain, and strong coupling, beyond expectation, of the fast electron jets with the return current through Cherenkov emission of plasmons. The hot electron energy scaling shows a strong dependence on intensity in the moderately relativistic domain I lambda(2) congruent to (10(18) - 10(20)) Wcm(-2) mu m(2), a scaling in vague accordance with current published estimates in the range I lambda(2) congruent to (0.14 - 3.5) x 10(21) Wcm(-2) mu m(2), and again a distinct power increase beyond I = 3.5 x 10(21) Wcm(-2) mu m(2). The low energy electrons penetrate normally to the target surface, the energetic electrons propagate in laser beam direction. (C) 2015 AIP Publishing LLC.

Laser ion acceleration (Wilks et al., 2001; Passoni et al., 2010) has become an interesting field of research in the past years. Several experiments, such as LIGHT (Schollmeier et al., 2008; Bagnoud et al., 2010; Busold et al., 2013; 2014a; 2014b) are performed worldwide. High intense, pulsed laser beams are used to generate and accelerate a plasma. For higher laser intensities (>10(21) W cm(-1)), simulations (Esirkepov et al., 2004; Macchi et al., 2005; 2009; 2010; Robinson et al., 2008; Rykovanov et al., 2008; Henig et al., 2009; Schlegel et al., 2009; Shoucri et al., 2011; 2013; 2014; Kar et al., 2012; Korzhimanov et al., 2012; Shoucri, 2012) have revealed a new acceleration mechanism: The Radiation Pressure Acceleration. The entire foil target is accelerated by the radiation pressure of the laser pulse. Ideally, a sharp peak spectrum is generated, with energies up to GeV and nearly solid body density. This work faces on a detailed analysis of the acceleration mechanism in order to develop the optimum laser- and target parameters for the process. The analysis is supported by one-dimensional PIC simulations, using the commercial code VSim((c)) Tech-X (2015).

It is proposed that laser hole-boring at a steady speed in inhomogeneous overdense plasma can be realized by the use of temporally tailored intense laser pulses, producing high-fluence quasi-monoenergetic ion beams. A general temporal profile of such laser pulses is formulated for arbitrary plasma density distribution. As an example, for a precompressed deuterium-tritium fusion target with an exponentially increasing density profile, its matched laser profile for steady hole-boring is given theoretically and verified numerically by particle-in-cell simulations. Furthermore, we propose to achieve fast ignition by the in-situ hole-boring accelerated ions using a tailored laser pulse. Simulations show that the effective energy fluence, conversion efficiency, energy spread, and collimation of the resulting ion beam can be significantly improved as compared to those found with un-tailored laser profiles. For the fusion fuel with an areal density of 1.5 g cm(-2), simulation indicates that it is promising to realize fast ion ignition by using a tailored driver pulse with energy about 65 kJ. (C) 2014 AIP Publishing LLC.

The standard picture of the Coulomb logarithm in the ideal plasma is controversial, the arguments for the lower cut off need revision. The two cases of far subthermal and of far superthermal electron drift motions are accessible to a rigorous analytical treatment. We show that the lower cut off bmin is a function of symmetry and shape of the shielding cloud, it is not universal. In the subthermal case, shielding is spherical and bmin is to be identified with the de Broglie wavelength; at superthermal drift the shielding cloud exhibits cylindrical (axial) symmetry and bmin is the classical parameter of perpendicular deflection. In both situations, the cut offs are determined by the electron-ion encounters at large collision parameters. This is in net contrast to the governing standard interpretation that attributes bmin to the Coulomb singularity at vanishing collision parameters b and, consequently, assigns it universal validity. The origin of the contradictions in the traditional picture is analyzed.

The Debye screening potential is generalized for an arbitrary isotropic distribution function and the dynamic screening for a cold streaming plasma is calculated. In both cases the structure of the screening length is the same, however the potentials are different. For the warm plasma under arbitrary drift the ballistic model is compared with the self consistent dielectric model. The validity of the Drude ansatz is shown to hold as long as the electron oscillations parallel to its motion are negligible. Their energy is by twice the Coulomb logarithm lower than in perpendicular direction. Finally, the problem of the Coulomb singularity is addressed. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Among the various attempts to model collisionless absorption of intense and superintense ultrashort laser pulses, the so-called Brunel mechanism plays an eminent role. A detailed analysis reveals essential aspects of collisionless absorption: Splitting of the electron energy spectrum into two groups under p-polarization, prompt generation of fast electrons during one laser cycle or a fraction of it, insensitivity of absorption with respect to target density well above nc, robustness, simplicity, and logical coherence. Such positive aspects contrast with a non-Maxwellian tail of the hot electrons, too low energy cut off, excessively high fraction of fast electrons, and inefficient absorption at moderate angles of single beam incidence and intensities. Brunel’s pioneering idea has been the recognition of the role of the space charges induced by the electron motion perpendicular to the target surface that make irreversibility possible. By setting the electrostatic fields inside the overdense target equal to zero, anharmonic resonance and mixing of layers leading to Maxwellianization are excluded. To what extent the real electron spectra and their scaling on laser intensity are the product of the interplay between Brunel’s mechanism and anharmonic resonance is still an open question.

Relativistic laser pulse propagation into homogeneous plasmas has been investigated as a function of plasma density. At first, the propagation features are compared systematically between relativistic transparency (RT) and hole-boring (HB). Paramountly, a considerably broad intermediate regime, namely the incomplete HB regime, has been found between the RT regime and the HB regime for an extremely intense circularly polarized (CP) pulse. In this regime HB proceeds in collaboration with RT, resulting in a much faster propagation speed and a higher cut-off energy of fast ions than in the classic HB regime. Similarly to the classic HB regime, formulae are presented to model the laser propagation and the ion acceleration according to the modified momentum flux balance in this incomplete HB regime. The simulations give the density boundary between this incomplete HB regime and the classic HB regime for CP pulses, which is crucial for estimating the maximum mean ion energy and the maximum conversion efficiency that can be achieved by the classic HB acceleration at a given laser intensity. For linear polarization (LP) the propagation mechanism apparently undergoes a transition in time between these two regimes. A detailed comparison between LP and circular polarization is made for these phenomena.

High-power laser pulse propagation in an overdense plasma due to the relativistic critical density increase has been investigated in one dimension. In a first step the conditions for the existence of a relativistic critical density are delimited and supported by particle-in-cell simulations. Its accurate determination is made possible by the installation of a new numerical diagnostics. Guided by this we show that the critical density increase strongly depends on both laser polarization and plasma density profile. Further, we find a new relaxation time ranging from several to many laser cycles, which sets a limit for short laser pulse manipulation and tailoring. Paramountly, it is proved that in the power optics domain the pulse propagation velocity is inhibited by the relativistic energy density in the medium and by the efficient reflection, in contrast to the group velocity from standard dispersion optics.

The transition from ablation to radiation pressure with increasing laser intensity in linear polarization is studied in a steady state model. At moderate intensities and laser wavelength λ up to Iλ2=1015–1016W/cm2μm2 the pressure is determined basically by the hot plasma and its flow dynamics. The contribution of the ponderomotive (radiative) potential to the total pressure is determined by plasma outflow inhibition which causes flow stagnation in the critical region and ablation pressure lowering already at ratios radiation/plasma pressure as low as a few percent. When approaching relativistic intensities the dominance of the ponderomotive pressure leads to a continuous transition from a I2/3 to I1 dependence. The location of this transition is governed by heat conduction into the dense target interior. We attribute the strong deviations of the measured exponents from 23 in the low intensity domain to energy losses also by electron heat flow. Basic features of the model have been tested by particle-in-cell simulations.

Sporadically, relativistic energies have been considered already in the foregoing chapters. As the laser flux density in the near infrared and visible long wavelength regime exceeds $$I\simeq 10^{18}\,{\textrm{Wcm}^{-2}}$$ , the electron quiver energy assumes relativistic values. A brief presentation of basic relativity may be useful here.