Reynaldo Castillo

Principle of high accuracy for the nonlinear theory of the acceleration of electrons in a vacuum by lasers at relativistic intensities

Acceleration of electrons by lasers in a vacuum was considered impossible based on the fact that plane-wave and phase symmetric wave packets cannot transfer energy to electrons apart from Thomson or Compton scattering or the Kapitza-Dirac effect. The nonlinear nature of the electrodynamic forces of the fields to the electrons, expressed as nonlinear forces including ponderomotion or the Lorentz force, permits an energy transfer if the conditions of plane waves in favor of the beams and/or the phase symmetry are broken. The resulting electron acceleration by lasers in a vacuum is now well understood as free wave acceleration, as ponderomotive scattering, as violent acceleration, or as vacuum beat wave acceleration. The basic understanding of these phenomena relates to an accuracy principle of nonlinearity for explaining numerous discrepancies on the way to the mentioned achievement of vacuum laser acceleration, which goes beyond the well-known experience of necessary accuracy in both modeling and experimental work experiences among theorists and experimentalists in the field of nonlinearity, From mathematically designed beam conditions, an absolute maximum of electron energy per laser interaction has been established. It is shown here how numerical results strongly (both essentially and gradually) depend on the accuracy of the used laser fields for which examples are presented and finally tested by the criterion of the absolute maximum.

Relativistic and ponderomotive self-focusing at laser–plasma interaction

The nonlinear plasma dielectric function due to relativistic electron motion is derived. From this, one can obtain the nonlinear refractive index of the plasma and estimate the importance of relativistic self-focusing in comparison with ponderomotive non-relativistic self-focusing at very high laser intensities. When the laser intensity is very high, ponderomotive self-focusing will be dominant. However, at some point, when the oscillating velocity of the plasma electrons becomes very large, relativistic effects will also play a role in self-focusing.

Focusing and defocusing of the nonlinear paraxial equation at laser–plasma interaction

This paper presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit T → 0 of the nonlinear paraxial equation at laser-plasma interaction. In a general setting of both dimension and nonlinearity, the essential differences between the focusing and defocusing cases is identified due to the nonlinearity, and dispersion effects involved in the propagation of solitons at laser plasma interaction. A sequence of codes has been developed in mathematics to explore the focusing and defocusing of the soliton formation and propagation.

Laser-generated pair production and Hawking-Unruh radiation

Laser-produced electron-positron pair production has been under discussion in the literature since 1969. Large numbers of positrons have been generated by lasers for a few years in studies which are also related to the studies of the physics of the fast ignitor laser fusion concept. For electron-positron pair production in vacuum due to vacuum polarization as predicted by Heisenberg (1934) with electrostatic fields, high-frequency laser fields with intensities around 10 28 W/cm 2 are necessary and may be available within a number of years. A similar electron acceleration by gravitation near black holes denoted as Hawking-Unruh radiation was discussed in 1985 by McDonald. The conditions are considered in view of the earlier work on pair production, change of statistics for electrons in relativistic black body radiation, and an Einstein recoil mechanism with a consequence of a physical foundation of the fine structure constant.

Numerical programming of self-focusing at laser-plasma interaction

This paper presents an investigation into the behavior of a laser beam of finite diameter in plasma with respect to forces and optical properties, which lead to self-focusing of the beam. The transient setting of ponderomotive nonlinearity in a collisionless plasma has been studied, and consequently the self-focusing of the pulse, and the focusing of the plasma wave occurs. The description of a self-focusing mechanism of laser radiation in the plasma due to nonlinear forces acting on the plasma in the lateral direction, relative to the laser has been investigated in the nonrelativistic regime. The behavior of the laser beams in plasma, which is the domain of self-focusing at high or moderate intensity, is dominated by the nonlinear force. The investigation of self-focusing processes of laser beams in plasma results from the relativistic mass and energy dependency of the refractive index at high laser intensities. Here, the relativistic effects are considered to evaluate the relativistic self-focusing lengths for the Nd glass radiation, at different plasma densities of various laser intensities. A numerical program in c + + that incorporates both the ponderomotive force in self-focusing mechanism and relativistic effects has been developed to explore in depth self-focusing over a wide range of parameters.

Review about acceleration of plasma by nonlinear forces from picoseond laser pulses and block generated fusion flame in uncompressed fuel

In addition to the matured “laser inertial fusion energy” with spherical compression and thermal ignition of deuteriumtritium (DT), a very new alternative for the fast ignition scheme may have now been opened by using side-on block ignition aiming beyond the DT-fusion with igniting the neutron-free reaction of proton-boron-11 (p- 11 B). Measurements with laser pulses of terawatt power and ps duration led to the discovery of an anomaly of interaction, if the prepulses are cut off by a factor 10 8 (contrast ratio) to avoid relativistic self focusing in agreement with preceding computations. Applying this to petawatt (PW) pulses for Bobin-Chu conditions of side-on ignition of solid fusion fuel results after several improvements in energy gains of 10,000. This is in contrast to the impossible laser-ignition of p- 11 B by the usual spherical compression and thermal ignition. The side-on ignition is less than ten times only more difficult than for DT ignition. This is essentially based on the instant and direct conversion the optical laser energy by the nonlinear force into extremely high plasma acceleration. Genuine two-fluid hydrodynamic computations for DT are presented showing details how ps laser pulses generate a fusion flame in solid state density with an increase of the density in the thin flame region. Densities four times higher are produced automatically confirming a RankineHugoniot shock wave process with an increasing thickness of the shock up to the nanosecond range and a shock velocity of 1500 km/s which is characteristic for these reactions.

Difference between Hawking and Unruh radiation derived from studies about pair production by lasers in vacuum

Laser acceleration of electrons in laser fields of intensities above 10 28 W/cm 2 were found to be in the same range as acceleration at the surface of black holes, where the laser intensities are in the range of pair production in vacuum due to vacuum polarization. The results in connection with the black holes arrived at similarities to the Hawking and Unruh radiation. We present here results based on the thermodynamics of the vacuum fluctuations that there is a difference between Hawking and Unruh effects in connection with the Casimir effect in view of the vacuum properties for laser produced pairs in a vacuum.

Proton-Metal Reactions in Thin Films with Boltzmann Distribution Similar to Nuclear Astrophysics

The proton reactions in host metals like palladium, nickel, or titanium generate elements up to a proton number Z = 82 (lead), where the generation probability follows a kind ofBoltzmann distribution. This is very similar to the standard abundance distribution of the elements in the universe for heavy elements. The analogy leads to a relation to the magic numbers of the nuclear shell model, to its alternative (more general) foundation on the Bagge series contrary to the spin model of Jensen and Goeppert-Mayer, and to new large magic numbers in agreement with Greiner et al.s results on superheavy elements.

Modeling diffusion in restricted systems using the heat kernel expansion

The averaged return-to-origin probability of finding a diffusing particle within a volume or in the neighborhood of the surface of a bounded region can be separated into a volume and a surface integral of the corresponding probability densities. However with the usual treatments (e.g., the commonly encountered diffusion propagator approach) there is no clear method to separate the integration of the diffusion propagators in each domain. Here we propose a general procedure based on applying the heat kernel expansion in restricted diffusion problems for the Greens function of the diffusion equation on an arbitrary region with an arbitrary boundary condition. We apply this method to the treatment of surface reaction rate in a sphere subject to the reflecting boundary condition. We determine that the rate of diffusion of a particle from the interior to the surface of the sphere changes by the square root of time plus some extra correction terms. Further, we are able to relate the diffusion propagator to the invariant properties of the region. Also in this approach we investigate how the heat kernel expansion can be applied to the problem of determining the return-to-origin probability, where we obtain a more precise result for the expansion of this probability in the case of a sphere. The advantage of this method lies in its generality and applicability to any geometrical boundary configuration and any kind of boundary condition.

Ultrahigh acceleration of plasma blocks from direct converting laser energy into motion by nonlinear forces

In contrast to thermal pressure, 100,000 times higher acceleration of plasma blocks was predicted and measured by using nonlinear (ponderomotive) forces. This permits side-on ignition of uncompressed solid fusion fuel deuterium-tritium and hydrogen-boron 11.