The inverse skin effect in the Z-pinch and plasma focus

The inverse skin effect and its influence on the dynamics of high-current Z-pinch and plasma focus discharges in deuterium are analyzed. It is shown that the second compression responsible for the major fraction of the neutron yield can be interpreted as a result of the inverse skin effect resulting in the axial concentration of the longitudinal current density and the appearance of a reversed current in the outer layers of plasma pinches. Possible conditions leading to the enhancement of the inverse skin effect and accessible for experimental verification by modern diagnostics are formulated.     

Collective ion acceleration during the decay of a high-current Z-pinch

A study is made of the Z-pinch plasma expansion after the current is switched off. Measurements were carried out in experiments on the implosion of tungsten wire arrays in the Angara-5-1 facility. It is found experimentally that, at a distance of 2 m from the pinch, the ion velocity in the expanding Z-pinch plasma is about (2.5–4.0) × 10⁷ cm/s, which substantially exceeds the thermal velocity of tungsten ions. A model describing the plasma expansion process is proposed that is based on the ambipolar acceleration mechanism. The results of numerical simulations are compared with the experimental data.     

Physicomathematical model of plasma acceleration in an ablative pulsed plasma thruster

A new comparatively simple quasi-one-dimensional physicomathematical model of plasma acceleration in an ablative pulsed plasma thruster with a capacitive energy storage is proposed. In spite of its simplicity, the model adequately reflects the main physical processes occurring in the thruster channel in the course of plasma blob acceleration: the blob dynamics, plasma radiation, absorption of radiation by the Teflon channel walls, ablation of the wall material, and plasma ionization. The results of computer simulations agree well with the experimental results.     

On the spectrum of Z-pinch plasma neutrons

Generation of neutrons from Z-pinch discharges in a deuterated gas medium has been studied. It is shown that a power-law energy dependence of the number of high-energy deuterons in Z-pinch plasma explains the observed broadening of the neutron spectrum in these systems. It is established that, at an average ion energy below 3 keV in Z-pinch plasma, neutrons are mostly generated due to the interaction of high-energy (∼100-keV) deuterons with the main plasma components.     

Electromagnetic acceleration of electron transfer reactions

The Moving Charge Interaction (MCI) model proposes that low frequency electromagnetic (EM) fields affect biochemical reactions through interaction with moving electrons. Thus, EM field activation of genes, and the synthesis of stress proteins, are initiated through EM field interaction with moving electrons in DNA. This idea is supported by studies showing that EM fields increase electron transfer rates in cytochrome oxidase. Also, in studies of the Na,K-ATPase reaction, estimates of the speed of the charges accelerated by EM fields suggest that they too are electrons. To demonstrate EM field effects on electron transfer in a simpler system, we have studied the classic oscillating Belousov--Zhabotinski (BZ) reaction. Under conditions where the BZ reaction oscillates at about 0.03 cycles/sec, a 60 Hz, 28 microT (280 mG) field accelerates the overall reaction. As observed in earlier studies, an increase in temperature accelerates the reaction and decreases the effect of EM fields on electron transfer. In all three reactions studied, EM fields accelerate electron transfer, and appear to compete with the intrinsic chemical forces driving the reactions. The MCI model provides a reasonable explanation of these observations.     

Nonquasineutral model of an equilibrium Z-pinch

A fundamentally new approach is proposed for describing Z-pinches when the pinch current is gov-erned to a large extent by strong charge separation, which gives rise to a radial electric field in the nonquasineutral core of the pinch. In the central pinch region with a characteristic radius of about $r_0 \sim \sqrt {J_0 /en_e c}$ , part of the total pinch current J ₀<J, is carried by the drifting electrons and the remaining current is carried by ions moving at the velocity v _iz ～c(2eZJ/m _i c ³) in the peripheral region with a radial size of c/ω_pi. In the nonquasineutral core of a Z-pinch, the radial ion “temperature” is on the order of ZeJ ₀/c. The time during which the non-quasineutral region exists is limited by Coulomb collisions between the ions oscillating in the radial direction and the electrons. Since the magnetic field is not frozen in the ions, no sausage instability can occur in the non-quasineutral core of the Z-pinch. In the equilibrium state under discussion, the ratio of the radial charge-separation electric field E ₀ to the atomic field E _a may be as large as $E_0 /E_a \sim 137^2 (a_0 \omega _{pe} /c)\sqrt {J/J_{Ae} }$ , where a ₀ is the Bohr radius.     

Stratification and filamentation mechanism for a multicharged plasma of a Z-pinch

The thermal-ionizational instability that gives rise to axial and azimuthal inhomogeneities in the electron temperature and electron density in the form of striations and filaments in a multicharged plasma of a Z-pinch is studied in the linear approximation. The theoretical results on the rate at which the inhomogeneities grow and their characteristic spatial dimension agree with the experimental data.     

Efficiency of ion acceleration by a relativistically strong laser pulse in an underdense plasma

A particle-in-cell simulation is used to investigate ion acceleration by a femtosecond laser pulse propagating in an underdense plasma slab. In plasma slabs with different thicknesses, the ions are found to be accelerated by different mechanisms. It is shown that, for laser pulse intensities in the range (5–10)×10¹⁹ W/cm², the ions are accelerated near the plasma-vacuum interface. __________ Translated from Fizika Plazmy, Vol. 27, No. 3, 2001, pp. 225–234. Original Russian Text Copyright ￠ 2001 by Kuznetsov, Esirkepov, Kamenets, Bulanov.     

Investigation of ion acceleration in an expanding laser plasma by using a hybrid Boltzmann-Vlasov-Poisson model

The acceleration of ions of different species from a plasma slab under the action of a charge-separation electric field driven by hot and cold electrons is studied by using a hybrid Boltzmann-Vlasov-Poisson model. The obtained spatial and energy distributions of light and heavy ions in different charge states demonstrate that the model can be efficiently used to study the ion composition in a multispecies expanding laser plasma. The regular features of the acceleration of ions of different species are investigated. The formation of compression and rarefaction waves in the halo of light ion impurity, as well as their effect on the energy spectrum of the accelerated ions, is analyzed. An approach is proposed that makes it possible to describe the production of fast ions by laser pulses of a given shape. It is shown that the energy of fast ions can be increased markedly by appropriately shaping the pulse. The effect of heating of the bulk of the cold target electrons on the ion acceleration is discussed.     

Dynamics of an Al wire corona of a megaampere Z-pinch

It is shown that the development of instabilities in a Z-pinch plasma formed by loading a relatively thick Al wire (an initial diameter of 120 μm and a maximum discharge current of 2–3 MA) is slowed down due to the high plasma density in the wire corona. A cylindrically symmetric, regular, and stable corona surrounding the wire contains a helical formation with a dense, cold, and magnetized plasma. X-ray pulses with a photon energy of several keV and an FWHM duration of 10–20 ns are generated by a few imploded neck structures in the pinch phase of the corona evolution (70–100 ns after the current onset). The main part of X radiation emitted by individual bright spots in the photon energy range 1.5–2.4 keV (up to 40 J at a peak power of 4 GW) consists of the continuum and the bound-bound transition radiation from H-and He-like Al ions. A possible scenario for the axial magnetic field evolution during an X-ray pulse is outlined. __________ Translated from Fizika Plazmy, Vol. 28, No. 4, 2002, pp. 329–336. Original Russian Text Copyright ? 2002 by Kubeš, Renner, Krousky, Kravárik, Bakshaev, Blinov, Chernenko, Gordeev, Dan’ko, Korolev, Shashkov.     

Electromagnetic wave in a relativistic magnetized plasma

Results are presented from a theoretical investigation of the dispersion properties of a relativistic plasma in which an electromagnetic wave propagates along an external magnetic field. The dielectric tensor in integral form is simplified by separating its imaginary and real parts. A dispersion relation for an electromagnetic wave is obtained that makes it possible to analyze the dispersion and collisionless damping of electromagnetic perturbations over a broad parameter range for both nonrelativistic and ultrarelativistic plasmas.     

Nonlinear inverse bremsstrahlung absorption in a photoionized plasma

Nonlinear inverse bremsstrahlung absorption is investigated for a plasma photoionized in the Bethe regime of suppression of the ionization barrier, in which case the electron velocity distribution coincides with the distribution of atomic electrons. A comparison is made between the characteristic features of absorption in the cases where atomic electrons before ionization are in the ns and np states. It is established that, in the case of np states, the effective high-frequency conductivity is always nonlinear; in particular, for weak pump fields, it is proportional to the square of the pump field strength. The maximum plasma conductivity associated with p electrons is one order of magnitude lower than the maximum effective conductivity associated with s electrons, which creates conditions for less efficient plasma heating through inverse bremsstrahlung absorption.     

Formation of hot spots in the plasma of a Z-pinch produced from low-density deuterated polyethylene

Results are presented from experimental studies of the plasma formation dynamics in a Z-pinch produced from a cylindrical microporous agar-agar load. The experiments were performed on the S-300 facility at a current of 2 MA and current rise time of 100 ns. To enhance the energy concentration, a deuterated polyethylene neck with a mass density of 50–75 μg/cm³ and diameter of 1–2 mm was made in the central part of the load. The spatiotemporal characteristics of the Z-pinch were studied using an optical streak camera and fast frame photography in the optical and soft X-ray spectral ranges. X-ray emission was detected using semiconductor and vacuum diodes, and neutron emission was studied by means of the time-of-flight method. It is found that, in the course of continuous plasma production, hot spots with a diameter of 100 μm form in the pinch plasma. The hot spots emit short soft X-ray pulses with a duration of 2–4 ns, as well as neutron pulses with an average neutron energy of about 2.45 MeV. The maximum neutron yield was found to be 4.5 × 10⁹ neutrons per shot. The scenario of hot spot formation is adequately described by two-dimensional MHD simulations.     

Ion acceleration in a dipole vortex in a laser plasma corona

Particle-in-cell simulations show that the inhomogeneity scale of the plasma produced in the interaction of high-power laser radiation with gas targets is of fundamental importance for ion acceleration. In a plasma slab with sharp boundaries, the quasistatic magnetic field and the associated electron vortex structure produced by fast electron beams both expand along the slab boundary in a direction perpendicular to the plasma density gradient, forming an extended region with a quasistatic electric field, in which the ions are accelerated. In a plasma with a smooth density distribution, the dipole magnetic field can propagate toward the lower plasma density in the propagation direction of the laser pulse. In this case, the electron density in an electric current filament at the axis of the magnetic dipole decreases to values at which the charge quasineutrality condition fails to hold. In electric fields generated by this process, the ions are accelerated to energies substantially higher than those characteristic of plasma configurations with sharp boundaries.     

Interferometric measurements of the plasma density at the Z-pinch periphery in the angara-5-1 facility

Knowledge of spatial mass distribution is important for understanding the physics of implosion of megaampere-current wire arrays. The paper presents results from studying the electron density distribution at the periphery of a tungsten wire array near the instant of maximum compression by using laser interferometry at λ=0.69 µm. It is found that, at the instant of maximum compression (～100 ns after the beginning of the discharge), the estimated maximum local electron density inside the wire array reaches ～10¹⁸ cm^?3 at a distance of 0.3–3 mm from the initial wire positions. Assuming the average tungsten ion charge to be 10, the local linear mass density in this region turns out to be 3 µg/cm, which amounts to about 10% of the total linear mass density of the liner. A fraction of the generator current flows through this plasma. The duration of the soft X-ray pulse is 5–8 ns, which indicates the achievement of a fairly high compression ratio.     

Effect of the longitudinal momentum of electrons on their surfatron acceleration by an electromagnetic wave in space plasma

By numerically calculating the second-order nonlinear time-dependent equation for the wave phase on a particle trajectory, the effect of the longitudinal (with respect to the external magnetic field) momentum of electrons on the dynamics of their surfatron acceleration by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed. It is shown that, for strongly relativistic initial values of the longitudinal component of the electron momentum (the other parameters of the problem being fixed), the electrons are trapped into the ultrarelativistic regime of surfatron acceleration within a definite interval of the initial wave phase Ψ(0) on the particle trajectory. It was assumed in the calculations that Ψ(0) ≤ π. For the initial wave phases lying within the interval of 0 < Ψ(0) ≤ π, the electrons are immediately trapped by the wave, whereas at π ≤ Ψ(0) ≤ 0, no electron trapping is observed even at long computation times. This result substantially simplifies estimates of the wave damping caused by particle acceleration. The dynamics of the velocity components, momentum, and relativistic factor of electrons in the course of their ultrarelativistic acceleration are considered. The obtained results present interest for the development of modern concepts of the mechanisms for the generation of ultrarelativistic particles in space plasma, correct interpretation of experimental data on the flows of such particles, explanation of possible reasons for the deviation of the fast particle spectra observed in the heliosphere from the standard power-law scaling, and analysis of the relation between such deviations and the space weather.     

Magnetic geometry, plasma profiles, and stability

The history of the stability of short wavelength modes, such as MHD instabilities and drift waves, has been a long and tortuous one as increasingly realistic representations of the equilibrium magnetic geometry have been introduced. Early work began with simple slab or cylindrical models where plasma profiles and magnetic shear were seen to play key roles. Then the effects of toroidal geometry, in particular the constraints imposed by periodicity in the presence of magnetic shear, provided a challenge for theory, which was met by the ballooning transformation. More recently the limitations on the conventional ballooning theory arising from effects such as toroidal rotation shear, low magnetic shear, and the presence of the plasma edge have been recognized. These have led in turn to modifications and extensions of this theory. These developments have produced a continuously changing view of the stability of the “universal” drift wave, for example. After a survey of this background, we describe more recent work of relevance to currently important topics, such as transport barriers characterized by the presence of strong rotation shear and low magnetic shear and the edge localized modes that occur in H-mode. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 7, pp. 588–598. Based on an invited talk given at the 11th European Fusion Theory Meeting, Aix-en-Provence, France, September 2005. The text was submitted by the author in English.     

Electromagnetic oscillations near the critical surface in a magnetized plasma

It is shown that, in a plasma whose density varies across the magnetic field lines, electromagnetic oscillations that are localized near the critical surface can exist. Such oscillations can be excited spontaneously in a nonequilibrium plasma of closed magnetic confinement systems.     

Inertial compensation for belt acceleration in an instrumented treadmill

Instrumented treadmills provide a convenient means for applying horizontal perturbations during gait or standing. However, varying the treadmill belt speed introduces inertial artifacts in the sagittal plane moment component of the ground reaction force. Here we present a compensation method based on a second-order dynamic model that predicts inertial pitch moment from belt acceleration. The method was tested experimentally on an unloaded treadmill at a slow belt speed with small random variations (1.20±0.10 m/s) and at a faster belt speed with large random variations (2.00±0.50 m/s). Inertial artifacts of up to 12 Nm (root-mean-square, RMS) and 30 Nm (peak) were observed. Coefficients of the model were calibrated on one trial and then used to predict and compensate the pitch moment of another trial with different random variations. Coefficients of determination (R²$R^2$) were 72.08% and 96.75% for the slow and fast conditions, respectively. After compensation, the root-mean-square (RMS) of the inertial artifact was reduced by 47.37% for the slow speed and 81.98% for fast speed, leaving only 1.5 Nm and 2.1 Nm of artifact uncorrected, respectively. It was concluded that the compensation technique reduced inertial errors substantially, thereby improving the accuracy in joint moment calculations on an instrumented treadmill with varying belt speed.     

Computational issues of importance to the inverse recovery of epicardial potentials in a realistic heart-torso geometry

In vitro data from a realistic-geometry electrolytic tank were used to demonstrate the consequences of computational issues critical to the ill-posed inverse problem in electrocardiography. The boundary element method was used to discretize the relationship between the body surface potentials and epicardial cage potentials. Variants of Tikhonov regularization were used to stabilize the inversion of the body surface potentials in order to reconstruct the epicardial surface potentials. The computational issues investigated were (1) computation of the regularization parameter; (2) effects of inaccuracy in locating the position of the heart; and (3) incorporation of a priori information on the properties of epicardial potentials into the regularization methodology. Two methods were suggested by which a priori information could be incorporated into the regularization formulation: (1) use of an estimate of the epicardial potential distribution everywhere on the surface and (2) use of regional bounds on the excursion of the potential. Results indicate that the a posteriori technique called CRESO, developed by Colli Franzone and coworkers, most consistently derives the regularization parameter closest to the optimal parameter for this experimental situation. The sensitivity of the inverse computation in a realistic-geometry torso to inaccuracies in estimating heart position are consistent with results from the eccentric spheres model; errors of 1 cm are well tolerated, but errors of 2 cm or greater result in a loss of position and amplitude information. Finally, estimates and bounds based on accurate, known information successfully lower the relative error associated with the inverse and have the potential to significantly enhance the amplitude and feature position information obtainable from the inverse-reconstructed epicardial potential map.