Dielectric permittivity of quantum plasma. Part II

The transverse and longitudinal dielectric permittivities of isotropic quantum plasma are calculated in the quantum plasma models based on the Dirac and Pauli equations. The dispersion relations for transverse-longitudinal waves in quantum particle beams are derived. Relativistic longitudinal and transverse waves in cold isotropic quantum plasma in models based on the Klein-Gordon and Dirac equations, as well as spin waves in the model based on the Pauli equation, are considered. Conditions for wave-particle resonance interactions in relativistic quantum plasma are analyzed.     

Dielectric permittivity of quantum plasma. Part I

Collisionless quantum plasma models based on the Schröbinger, Klein-Gordon, Dirac, and Pauli equations are considered. The transverse and longitudinal dielectric permittivities of isotropic quantum plasma are calculated in the frameworks of the models based on the Schröbinger and Klein-Gordon equations without allowance for the particle spin. Dispersion relations for transverse-longitudinal waves in beams of spinless quantum particles are derived, and the simplest quantum waves are analyzed.     

Magnetic susceptibility and Landau diamagnetism of quantum collisional plasma

Quantum collisional plasma with an arbitrary degree of degeneracy of the electron gas is considered. Using the exact expression for the transverse electric conductivity of quantum collisional plasma, the magnetic susceptibility is described using the kinetic approach and a formula for calculating Landau diamagnetism is derived. Quantum Maxwellian plasma is considered as a special case. To this end, in the formulas derived, the limit is taken for the chemical potential tending to minus infinity. The properties of the magnetic susceptibility of quantum plasma are compared to those of degenerate and Maxwellian plasmas.     

Transverse permittivity of quantum collisional plasma with an arbitrary collision frequency

Expressions for the transverse permittivity of quantum collisional plasma with an arbitrary collision frequency depending on the momentum (wave vector) of plasma particles are derived in the framework of the Mermin approach by using the kinetic Schröbinger-Boltzmann equation with a collision integral in the relaxation approximation in momentum space. It is shown that, when the collision frequency is constant, the derived expressions take the well-known form. The case of degenerate plasma in which the collision frequency is proportional to the absolute value of the wave vector is analyzed. This case corresponds to the assumption of a constant mean free path of plasma particles. The real and imaginary parts of the plasma permittivity are analyzed graphically.     

Quantum Theory of Surface Plasmon Polaritons: Planar and Spherical Geometries

A quantum theory of retarded surface plasmons on a metal–vacuum interface is formulated, by analogy with the well-known and widely exploited theory of exciton-polaritons. The Hamiltonian for mutually interacting instantaneous surface plasmons and transverse electromagnetic modes is diagonalized with recourse to a Hopfield–Bogoljubov transformation, in order to obtain a new family of modes, to be identified with retarded plasmons. The interaction with nearby dipolar emitters is treated with a full quantum formalism based on a general definition of modal effective volumes. The illustrative cases of a planar surface and of a spherical nanoparticle are considered in detail. In the ideal situation of absence of dissipation, as an effect of the conservation of in-plane wavevector, retarded plasmons on a planar surface represent true stationary states (which are usually called surface plasmon polaritons), whereas retarded plasmons in a spherical nanoparticle, characterized by frequencies that overlap with the transverse electromagnetic continuum, become resonances with a finite radiative broadening. The theory presented constitutes a suitable full quantum framework for the study of nonperturbative and nonlinear effects in plasmonic nanosystems.     

Immunological and biochemical properties of transverse tubule membranes isolated from rabbit skeletal muscle

A new method for isolating transverse tubule membranes from rabbit skeletal muscle has been developed. This procedure has the advantage of being mild, fast, and producing with good yields a purified membrane fraction. The transverse tubule membranes are purified by a discontinuous sucrose density centrifugation after loading contaminating light sarcoplasmic reticulum vesicles with calcium phosphate in the presence of ATP. Immunofluorescence staining of cryostat sections of rabbit psoas muscle with purified goat antibodies directed against the purified membranes shows that the reacting antigens are distributed at the boundary of the A and I bands of the myofibrils where transverse tubules are localized in mammalian muscle. The purified antibodies showed no cross-reactivity with sarcoplasmic reticulum, nor did they show any fluorescence staining of the muscle plasma membrane, indicating that the isolated membranes indeed originate from the transverse tubules. The transverse tubule fraction has a characteristic protein composition distinguishable from that of sarcoplasmic reticulum, a much higher cholesterol content than that of the crude microsomes, plasma membrane, and sarcoplasmic reticulum, and a phospholipid content about twice as high as that of sarcoplasmic reticulum and plasma membrane. The purified transverse tubule membrane has a distinct phospholipid composition with high contents of sphingomyelin and phosphatidylserine. A Mg2+-activated ATPase characteristic of the transverse tubule fraction undergoes a 20-30-fold increase in specific activity during purification. The levels of Ca2+-ATPase activity present in the purified transverse tubule fraction remain comparable to those of sarcoplasmic reticulum even after extensive removal of the latter.     

Study of nonneutral plasma storage in a magnetic trap with a rotating electric field at the lepta facility

Results from experimental studies of plasma storage in a Penning-Malmberg trap at the LEPTA facility are presented. The number of stored particles is found to increase substantially when using the so-called “rotating wall” method, in which a transverse rotating electric field generated by a cylindrical segmented electrode cut into four pairs is applied to the plasma storage region. The conditions of transverse compression of the plasma bunch under the action of the rotating field and buffer gas are studied. The optimal storage parameters are determined for these experimental conditions. Mechanisms of the action of the rotating field and buffer gas on the process of plasma storage are discussed.     

Influence of resonant charge exchange on the viscosity of partially ionized plasma in a magnetic field

The influence of resonant charge exchange for ion-atom interaction on the viscosity of partially ionized plasma embedded in the magnetic field is investigated. The general system of equations used to derive the viscosity coefficients for an arbitrary plasma component in the 21-moment approximation of Grad’s method is presented. The expressions for the coefficients of total and partial viscosities of a multicomponent partially ionized plasma in the magnetic field are obtained. As an example, the coefficients of the parallel and transverse viscosities for the ionic and neutral components of the partially ionized hydrogen plasma are calculated. It is shown that the account for resonant charge exchange can lead to a substantial change of the parallel and transverse viscosity of the plasma components in the region of low degrees of ionization on the order of 0.1.     

Distinctive features of collisionless gradient drift instabilities in a high-β plasma in a highly nonuniform magnetic field

A set of Vlasov-Maxwell equations for collisionless electromagnetic drift instabilities of high-β plasma configurations with a nonuniform magnetic fields is solved. The effect of the transverse static magnetic field variation and magnetic field line curvature, as well as the plasma temperature and density gradients, is considered. It is shown that, in a nonuniform magnetic field, the behavior of the instabilities differs substantially from that in a uniform field. Electromagnetic modes propagating strictly transverse to the lines of the static magnetic field are analyzed in detail, and unstable solutions are obtained for both extraordinary and ordinary waves. Numerical results show that, in the latter case, instability occurs when the magnetic field decreases toward the periphery and the plasma temperature and density gradients are oppositely directed.     

Configuration of an inviscid plasma in the field of a rotating magnetized central body

The problem is considered of configurations of a strongly magnetized inviscid plasma around a rotating magnetized central body. Strong plasma magnetization implies that the Hall conductivity is much lower than the transverse conductivity, which in turn is much lower than the longitudinal conductivity. For such conditions, a self-consistent set of equations is derived that describes the conduction current density, the magnetic and electric fields, and the angular frequency of the plasma rotation under the assumptions that the components of the dielectric tensor of the plasma envelope are known functions of height and that the plasma mass velocity has only the azimuthal component. Under the assumption that the transverse conductivity is constant over a magnetic surface, the nonlinear equations derived are solved in quadratures within the class of angular frequency distributions that are symmetric about the equatorial plane. A particular solution for the plasma configurations in a dipole magnetic field is considered that corresponds to a model exponential dependence of the transverse conductivity on the number of the L-envelope (or, equivalently, on the number of the unperturbed magnetic surface).     

Classical and quantum description of electron trapping during the Cherenkov beam instability in plasma

A nonlinear quantum theory of the Cherenkov instability of a nonrelativistic monoenergetic electron beam in a cold plasma is constructed. It is shown that the instability of a low-density beam is almost purely quantum in nature and results from the emission of one quantum of a plasma wave—a plasmon—by the beam electrons. The number of emitted (and absorbed) plasmons increases with beam density, so, in the limit of high-density beams, the instability becomes a classical Cherenkov beam instability in plasma. Some analytic solutions and estimates are found, detailed numerical results are obtained, and the evolution of the quantum distribution function of the beam electrons in different regimes of the beam instability is investigated.     

Nonlinear relativistic quantum theory of Cherenkov emission of longitudinal Langmuir waves in a plasma

A nonlinear relativistic quantum theory of stimulated Cherenkov emission of longitudinal waves by a relativistic monoenergetic electron beam in a cold isotropic plasma is presented. The theory makes use of a quantum model based on the Klein-Gordon equation. The instability growth rates are obtained in the linear approximation and are shown to go over to the familiar growth rates in the classical limit. The mechanisms for the nonlinear saturation of relativistic Cherenkov beam instabilities are described with allowance for quantum effects, and the corresponding analytic solutions are derived.     

Instabilities of a circularly polarized wave with trapped particles in an isotropic plasma

The structure and stability of a transverse electromagnetic wave propagating with a velocity lower than the speed of light in an unmagnetized plasma are considered. The stationary finite-amplitude wave is described by exact solutions to the Vlasov-Maxwell equations. However, unlike the well-known electrostatic analog, the Bernstein-Greene-Kruskal wave, the wave structure is determined to a large extent by the presence of trapped particles with a shear of transverse velocities, without which the existence of waves with a refraction index larger than unity is impossible. It is shown that the main origin of the wave instability is the longitudinal motion of trapped particles relative to the background plasma. Expressions for the growth rates in the main instability regimes are found under definite restrictions on the wave parameters.     

Stability of Alfvén modes in a collisionless anisotropic plasma confined by a highly curved magnetic field

The stability of Alfvén modes in a collisionless plasma with an anisotropic pressure in a highly curved magnetic field is studied. A linearized equation for describing longitudinally nonuniform MHD perturbations with frequencies below the bounce frequency is derived. In this equation, the perturbations of longitudinal and transverse pressures are calculated using a collisionless kinetic equation. It is shown that longitudinal fluxes of the transverse and longitudinal plasma energies give rise to pressure perturbations different from those in the Chew-Goldberger-Low collisionless hydrodynamics. The corresponding energy principle is constructed. A stability criterion for Alfvén modes is obtained and is found to be more stringent than that in the Chew-Gold-berger-Low model.     

Quantum theory of Cherenkov beam instabilities in plasma

A quantum theory of stimulated Cherenkov emission of longitudinal waves by an electron beam in an isotropic plasma is presented. The emitted radiation is interpreted as instability due to the decay of the de Broglie wave of a beam electron. Nonrelativistic and relativistic nonlinear quantum equations for Cherenkov beam instabilities are obtained. A linear approximation is used to derive quantum dispersion relations and to determine the instability growth rates. The mechanisms for nonlinear saturation of quantum Cherenkov beam instabilities are investigated, and the corresponding analytic solutions are found.     

Magnetohydrodynamics of a weakly ionized plasma: Ambipolar magnetic diffusion and shock front structure

Kinetic equations with the BGK collision integral are used to derive MHD equations for a weakly ionized plasma that are applicable over a broad range of magnetic field strengths. In strong magnetic fields, a substantial contribution to the transverse diffusion of the magnetic field comes from the ambipolar magnetic diffusion, which is associated with the motion of both the charged component and the magnetic field against the background of the neutral plasma component. The problems of the magnetic field diffusion in a weakly ionized plasma and the shock wave structure are solved.     

Nonlinear properties of two-dimensional wake waves excited by relativistic electron bunches in plasma

The properties of a nonlinear plasma wake wave excited by an axially symmetric relativistic electron bunch are studied. It is shown that the nonlinear dependence of the wake wavelength on the transverse coordinate leads to distortion of the phase front of the wake wave and to steepening and oscillations of the transverse profile of the wakefield. The magnetic field of the wake wave is nonzero and oscillates at a frequency higher than the plasma electron frequency. Because of nonlinearity, the amplitude of the excited wake wave changes with distance from the bunch. The increase in nonlinearity leads to the development of turbulence and chaotization of the wakefield and results in the switching-on of the thermal effects and plasma heating.     

Nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in a dielectric medium

A nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in an isotropic dielectric medium is presented. A quantum model based on the Klein-Gordon equation is used. The growth rates of beam instabilities caused by the effect of stimulated Cherenkov radiation have been determined in the linear approximation. Mechanisms of the nonlinear saturation of relativistic quantum Cherenkov beam instabilities have been analyzed and the corresponding analytical solutions have been obtained.     

MHD stability of a collisionless anisotropic plasma in a system with an internal conductor

A study is made of the MHD stability of a collisionless anisotropic-pressure plasma in a nonparaxial magnetic configuration with an internal conductor in cylindrical geometry. A stability criterion for flutelike modes is obtained, and the families of marginally stable profiles of the longitudinal and transverse plasma pressures are calculated by using the Chew-Goldberger-Low anisotropic MHD equations. Possible marginally stable plasma states are considered with allowance for the expected turbulent relaxation and self-organization processes, on the one hand, and isotropization processes, on the other. A stability criterion for Alfvén modes is also derived in the Chew-Goldberger-Low model.     

Langmuir vacuum and superconductivity

It is shown that, in the ??jelly?? model of cold electron-ion plasma, the interaction between electrons and the quantum electromagnetic vacuum of Langmuir waves involves plasma superconductivity with an energy gap proportional to the energy of the Langmuir quantum.