Propagation and spreading of unstable perturbations in electron-hole plasmas subject to crossed fields

A model is developed for electrostatic drift instabilities which arise in inhomogeneous electron-hole plasmas subject to crossed fieldsE ₀B ₀. The instabilities are initiated by gradients in the equilibrium plasma densityn ₀. Using two-fluid magnetohydrodynamics and linear perturbation theory the dispersion relation of local density oscillations is calculated for arbitrary inhomogeneous equilibrium distributions and plasma densities. For cases wheren ₀B ₀ andn ₀ ⁺ n ₀ ^- it is found that the propagation direction of maximal gain, , is the bisectrix of the angle between (–n ₀) and (E ₀ ×B ₀) and that stable and unstable configurations are distinguished by the angle between ₀ andn ₀. A local density perturbation built by superpositions of the plane waves, and initially chosen radially symmetric, broadens unisotropically. In the direction transverse to the broadening is anomaleously enhanced, as compared to the broadening by diffusion in the stable case. The results are referred to experimental observations of low-frequency instabilities reported in [1].     

Low-frequency instability of an inhomogeneous weakly ionized plasma in crossed electric and inhomogeneous magnetic fields

The paper discusses the drift dissipative instability that arises in a weakly ionized inhomogeneous plasma in crossed electric and magnetic fields. The potential perturbations are studied in the WKB (Wentzel-Krammers-Brillouin) approximation, i.e. for k = d lnn ₀/dx. The critical magnetic field, beyond the value of which the plasma is again stable against the studied perturbations, is computed. The effect of the inhomogeneity of the magnetic field modelled by a gravitational field is analyzed and the effect of a magnetic field, growing in the direction opposite to that of the plasma density, is pointed out. Under certain circumstances similar phenomena also arise in the current-convective instability.The author wishes to express his thanks to J. Václavík, K. Jungwirth and J. Preinhaelter for their stimulating discussions and comments.     

Effect of Temperature Anisotropy on Various Modes and Instabilities for a Magnetized Non-relativistic Bi-Maxwellian Plasma

Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those modes whose magnetic-field perturbations are perpendicular to the ambient magnetic field, i.e., B ₁ $\bot $ B ₀, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them (i.e., the whistler mode, pure Alfvén mode, firehose instability, and whistler instability), and the O-mode are affected by thermal anisotropies, since they satisfy the required condition $\mathbf{B}_{1}\bot \mathbf{B}_{0}$ . By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfvén waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations. The threshold conditions for different instabilities are also obtained.     

Direct gauging of the Poincaré group V. Group scaling,classical gauge theory,and gravitational corrections

Homogeneous scaling of the group space of the Poincaré group,P ₁₀, is shown to induce scalings of all geometric quantities associated with the local action ofP ₁₀. The field equations for both the translation and the Lorentz rotation compensating fields reduce toO(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8Gc ^–4. Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to breakP ₁₀-gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system ofP ₁₀-gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincaré gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable.     

Direct gauging of the Poincaré group. II

This paper continues the study of direct gauge theory of the Poincaré groupP ₁₀. The meanings and implications of transformations induced by the local action ofP ₁₀ are studied, and transformation rules for all field quantities are derived for the local action ofP ₁₀ in a sufficiently small neighborhood of the identity. These results lead directly to a system of fundamental partial differential equations that are both necessary and sufficient for invariance of the free field Lagrangian density. Homogeneity arguments and the classical theory of invariants are used to obtain the most general free field Lagrangian density. Gauge conditions are shown to imply coordinate conditions, and an algebraic system of antiexact gauge conditions is implemented. The underlying Minkowski space,M ₄, and the resulting Riemann-Cartan space,U ₄, become attached at their centers, as do their respective frame and coframe bundles. Weak constraints of vanishing torsion are studied. All field quantities are shown to be determined in terms of the compensating l-forms for the Lorentz sector alone provided an explicit system of integrability conditions is satisfied. Field equations of the Einstein type are shown to result.     

Nonlinear response and chaos in semiconductors induced by impact ionization

A review is given of the nonlinear response and chaos induced by impact ionization of neutral shallow donors, observed in n-GaAs. Two kinds of the observation are described; (i) firing wave instability, and (ii) periodically driven current filament. For the firing wave instability, several important aspects are discussed including the selective excitation of the current filaments and the deterministic nature of the firing density wave. The nonlinear response of a periodically driven current filament has been investigated by applying a dc+ac bias of the form ofV _dc+V _ac sin(2f ₀ t), wheref ₀1 MHz. The carrier dynamics and the bifurcation routes to chaos are discussed in terms of the observed phase diagram and the bifurcation map. The deterministic nature of the strange attractors are described in detail in terms of the correlation dimension and the Kolmogorov entropy.     

Experimental proof of mirror instabilities in the Isar I theta pinch

In the Isar I linear theta pinchm=0 instabilities were observed and experimentally investigated. The variation of the plasma parameters over a wide range (τ _ii =10^?2... 10²μsec) showed that them=0 instabilities only occurred in sufficiently hot and thin plasmas, and so they are most probably due to the anisotropic pressure of the ions and should be mirror instabilities. Perturbations of the plasma limited in space and time were observed by measuring the continuum radiation, by 90 ° laser scattering measurements and by measuring the magnetic field and the local neutron rate. All measurements showed distinct, correlated, local perturbations of the plasma cylinder. These perturbations were accompanied by bulging of the plasma cylinder and increasing density. The extent in the axial direction was of the order of the plasma diameter. It may be assumed that the observed instabilities contribute appreciably to relaxation of the anisotropic ion pressure and increase the end losses.     

Instability of two counter-streaming gyrating beams of electrons

The linear theory of the two-beam instability of weak gyrating beams is investigated. Maximum growth rates of instabilities, instability limits and frequencies of unstable waves are numerically determined. The aperiodic instability withk _{z z0}= _c( _z0 is the velocity of the beam along the magnetic field, _c is the cyclotron frequency andk _z is the longitudinal wave number) and the instability with= _c/2 and withk _{z z0}= _c/2 possess greatest growth rates. Dependence of growth rates on longitudinal and transversal components of the wave vector is investigated in detail.     

Planar ferromagnets: Low-velocity kink dynamics near to the easy plane and static solitary spin structures bifurcating from the azimuthal kink

Ferromagnetic spin chains with planar single ion anisotropy, exchange anisotropy and with an external fieldb applied in the easy plane are considered in classical continuum approximation. It is pointed out that in the static case the sine-Gordon approximation is only accidentally exact: it breaks down in the neighborhood of the easy plane already for infinitesimal kink velocities, unlessb0. It is also shown that at certain valuesb _n ,n=0, 1, 2, 3, ... of the applied field there bifurcate from the static in-plane kink (azimuthal kink) other static out-of-plane kink solutions. The azimuthal kink is linearly stable below the critical strengthb ₀ of the applied field. For increasingb, there occurs at each of the bifurcation fieldsb ₁<b ₂<b ₃... an instability with respect to an additional mode. In the undamped system the instabilities atb _2k ,k=0, 1, 2, ... are associated with the recently discovered soft-velocity change mechanism of the critical slowing-down, whereas atb _2k+1 , soft localized dynamic modes occur. If phenomenological spin damping is included, soft relaxation modes occur in the neighborhood of all the bifurcation fields.Work supported by the Swiss National Science Foundation     

The microwave Hall effect of a two-dimensional electron gas

The integer Quantum Hall effect has been recently observed in the Hall conductivity _xy at microwave frequencies. Here we present a calculation of the wave propagation in the crossed waveguide system used in the experiments. The field pattern is more complicated than in the case of a pure plane wave. The essential result, however, remains unchanged: The field strength in the second (crossed) waveguide is proportional to _xy of the two-dimensional electron gas. Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Convective excitation of quasistatic waves in an inhomogeneous anisotropic plasma

Local as well as surface waves excited in a streamingless plasma are investigated. In addition to the gradient instabilities of an isothermal plasma now branches of a convective type are found in plasmas with a hot electron componentZ T _e T _i . Both their frequencies and growth rates may exceed the ion cyclotron frequency, > _Bi even if the effect of the finite ion Larmor radius is negligible. Then the surface waves may become of enhanced importance. We compare, therefore, the conditions for excitation and the growth rates of the surface waves with those of the short wavelength (local) perturbations. Upper estimates of the saturated wave amplitudes are also given. For a special profile of the plasma density the problem is solved analytically also in the plasma boundary layer.On leave of absence from the Physical and Technical Institute, Kharkov, U.S.S.R.     

Symmetries of Einstein-Yang-Mills fields and dimensional reduction

LetE be a manifold on which a compact Lie groupS acts simply (all orbits of the same type);E can be written locally asM×S/I,M being the manifold of orbits (space-time) andI a typical isotropy group for theS action. We study the geometrical structure given by anS-invariant metric and anS-invariant Yang Mills field onE with gauge groupR. We show that there is a one to one correspondence between such structures and quadruplets of fields defined solely onM; _v is a metric onM,h are scalar fields characterizing the geometry of the orbits (internal spaces), ⁱ are other scalar fields (Higgs fields) characterizing theS invariance of the Lie(R)-valued Yang Mills field and is a Yang Mills field for the gauge groupN(I)|I×Z((I)),N(I) being the normalizer ofI inS, is a homomorphism ofI intoR associated to theS action, andZ((I)) is the centralizer of(I) inR. We express the Einstein-Yang-Mills Lagrangian ofE in terms of the component fields onM. Examples and model building recipes are given.     

Some superconducting properties of 25%Nb–75%Zr alloy

The manner of preparation of superconducting 25% wt Nb–75% wt Zr wires is described. Short samples of these wires were measured in static magnetic fields up to 80·5 kG and the authors describe the method of these measurements. The paper gives the results of measuring the critical current density dependence on the external perpendicular magnetic field for both cold-worked wires with different deformations and heat-treated wires. The dependence of the critical current density on the heat treatment temperature after wire deformation for different magnetic fields was obtained. The optimum heat treatment temperature (vacuum better than 10^–3 torr, 1 hour) is 450–600C for magnetic fields 0–80·5 kG. The values ofi _c of these wires in magnetic fields up to 60 kG are the same or higher than those of 75% Nb-25% Zr wires, and in fields above 60 kG they are much higher.     

Direct gauging of the poincaré group. III. Interactions with internal symmetries

The problem of gauging matter fields with a Poincaré invariant action functional that admits anr parameter, semisimple groupG(r) of internal symmetries is considered. A minimal replacement operator for the total groupP ₁₀×G(r) is obtained, together with the requisite compensating 1-forms for both the Poincaré and theG(r) sectors. A basis forP ₁₀×G(r)-invariant Lagrangian densities for the free fields is obtained. Restriction to Lagrangian densities that are at most quadratic in the associated curvature and torsion fields eliminates active coupling between theP ₁₀ free field Lagrangian and theG(r) free field Lagrangian, although there is passive coupling that arises through the requirement of tensorial covariance under general coordinate transformations generated by the local action of the translation group. A superposition principle, modulo passive coupling, thus holds for quadratic free field Lagrangian for the total group:L _TOT=L _P +L _G(r) . Field equations for the matter fields and the compensating fields of theG(r) sector are obtained. Both share the passive coupling toP ₁₀ that is required in order to achieve tensorial covariance, but only the matter fields couple directly to the Poincaré fields and only to the Lorentz sector. For weak Poincaré fields, the field equations for the matter fields and the compensating fields of the internal symmetries go over into the standard field equations of gauge theory for an internal symmetry group.     

Transport of meso-scale structures in tokamak edge plasmas

We review possible mechanisms of blobby transport in fusion-related plasmas. The models dealing with the effective plasma gravity and caused by both T _e and parallel shear of E × B drift instabilities are considered.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Instabilities of an electron cloud in a Penning trap

We have measured the storage instabilities of electrons in a Penning trap at low magnetic fields. These measurements are carried out as a function of the trapping voltage, for different magnetic fields. It is seen that these instabilities occur at the same positions when the trapping voltage is expressed as a percentage of the maximum voltage, given by the stability limit. The characteristic frequencies at which these instabilities occur, obey a relation that is given by n _zω _z + n ₊ω ₊ + n _-ω _- = 0, where ω _z, ω ₊ and ω _- are the axial, perturbed cyclotron and the magnetron frequencies of the trapped electrons respectively, and the n's are integers. The reason for these instabilities are attributed to higher order static perturbations in the trapping potential. Received 5 August 2002 / Received in final form 14 October 2002 Published online 17 December 2002 RID="a" ID="a"Present address: Dept. of Physics, Rampurhat College, Rampurhat, Birbhum, West Bengal, India. RID="b" ID="b"e-mail: werth@mail.uni-mainz.de     

Influence of magnetic fields on taylor vortex formation in magnetic fluids

The flow of a magnetic fluid placed inside a small gap between concentric rotating cylinders is investigated for axial, radial and azimuthal magnetic fields. An equation of motion is derived phenomenologically to describe the hydrodynamics of magnetic fluids. Studied are the changes in the critical Taylor numberT _c and wave numberT _c which characterize the instability of primary circular Couette flow towards Taylor vortices. It is found that all above magnetic fields have a stabilizing effect on circular Couette flow and thatT _c increases or decreases, depending on the direction of the magnetic field. Besides this, the influence of the magnetic fields on the correlation length ₀, the wave number of maximal growthk _m and the linear growth rate amplitude ₀ is determined.     

A new kind of electron-lattice interaction and the kinetics of breaking high-T c and low-T c superconductivity via large thermal energy fluctuations of lattice particles

A novel kind of a strong electron-lattice interaction in high-T _c (HTSC's) and conventional low-T _c (LTSC's)superconductors mediated by short-lived large energy fluctuations (SLEF's) of lattice atoms (ions) of lifetime 10^–13–10^–12s, is considered and applied to the kinetics of thermal pair-breaking in the HTSC's and LTSC's. The transition from the superconducting (SC) state into a non-SC state at temperaturesT _c in HTSC's or LTSC's is caused by a great number of SC pair-SLEF collisions each of which breaks the local quantum coherence and creates a local instability of the SC state. Quantum macroscopic percolation-like phenomena appear in HTSC's or LTSC's and destroy the SC state atTT _c when the mean distance between the simultaneously existing SLEF-induced local instabilities becomes of the order of the SC coherence length . The transition temperaturesT _c and pairing energies 2 as well as coupling constants in HTSC's and LTSC's are calculated and linked with some material parameters (the elasticity modulus, Debye temperature, SC pair density, etc.) through a modification of our earlier proposed theory of SLEF's and electron-SLEF interactions (Phys. Rep.99, 237 (1983) and Phys. Rev. B33, 2983 (1986)). Quasi-2-dimensional properties of carriers in HTSC's and the 3-dimensional nature of SC electrons in LTSC's are taken into account. The obtained new exponential equations for 2 have pre-exponential factor _Fv _F/d determined by the Fermi velocityv _F and the interatomic distanced. The transition temperature shows only a weak, if at all, isotope in HTSC's and the conventional isotope effect in LTSC's, in agreement with observations. Numerical estimates ofT _c and 2 are in agreement with experimental data for both HTSC's and LTSC's. The comparison of HTSC and LTSC properties is discussed.     

Electronic properties of a Weyl semimetal in crossed magnetic and electric fields

The study of Weyl semimetals is one of the most challenging problems of condensed matter physics. These materials exhibit interesting properties in a magnetic field. In this work, we investigate the Landau bands and the density of states (DOS) oscillations in a Weyl semimetal in crossed magnetic and electric fields. An expression is obtained for the energy spectrum of the system using the following three different methods: an algebraic approach, a Lorentz shift-based approach, and a quasi-classical approach. It is interesting that the energy spectrum calculated in terms of the quasi-classical approach coincides with the spectrum obtained using the microscopic approaches. An electric field is shown to change the Landau bands radically. In addition, the classical motion of a three-dimensional Dirac fermion in crossed fields is studied. In the case of a Dirac spectrum, the longitudinal (with respect to magnetic field) component of momentum (p _z ∥ H) is shown to be an oscillating function of the magnetic field. When the electric field is v⊥H/c, the Landau levels collapse and the motion becomes fully linear in an unusual manner. In this case, the wavefunction of bulk states vanishes and only states with p _z = 0 are retained. An electric field affects the character of DOS oscillations. An analytical expression is obtained for the quantum capacitance in crossed fields in the cases of strong and weak electric fields. Thus, an electric field is an additional parameter for adjusting the diamagnetic properties of Weyl semimetals.     

Perturbed Angular Correlation Study of Magnetic and Electric Hyperfine Interactions at 111Cd in GdNi2 and SmNi2

The magnetic hyperfine field B _hf of the closed-shell probe nucleus ¹¹¹Cd in the C15 Laves phase RNi₂ (R= Gd, Sm) has been investigated as a function of temperature by perturbed angular correlation (PAC) spectroscopy. The saturation magnetic hyperfine fields at 10 K are B _hf=7.7(2) and 3.9(1) T for GdNi₂ and SmNi₂, respectively. Although the probe nucleus resides on the cubic rare-earth site, a strong axially symmetric electric quadrupole interaction (QI) is observed in the paramagnetic phase at T300 K. The possible relation of this unexpected QI to the structural instability of RNi₂ is discussed.