Convective excitation of quasistatic waves in an inhomogeneous anisothermic plasma II. Nonlinear estimates

Nonlinear effects stabilizing the convective instabilities excited in an anisothermic plasma (T _etT _i) at the plasma boundaryaV_s/ _Bi) are discussed. Waves having in the linear theory (Part I) the highest growth rates ( _Bi) saturate at first. Being excited by a small part of slow plasma electrons ( _zTe) only, they saturate at a relatively low level. Further, surface waves with lower frequencies and higher phase velocities ( _ph/k_z) become dominant and a broadening of the plasma boundary occurs. For their saturation nonlinear interaction is more important than the quasilinear effects. During the time interval of several _Bi ^–1 the longest surface waves withk _yBi/V_s, _Bik_yV_s and _{ph Te} saturate at the absolutely highest level. The plasma boundary broadens in the meanwhile up toaV _s/_Bi. The wave energy is comparable to the whole energy connected with the longitudinal motion of the initially thermal electrons inside this boundary layer. The wave amplitude is large enough to trap the initially cold ions belonging to this layer and heat them up to energies comparable to those of the electron component. The heating process occurs again within several _Bi ^–1 and the Larmor radius of the ions is then comparable toV _s/_Bi. Further evolution of the system is governed by the unstable local perturbations.He leaves of absence from thePhysical and Technical Institute, Kharkov, USSR.     

Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

On the dynamics of a quantum system which is classically chaotic

We investigate the dynamics of one anisotropic spin in an external time-dependent magnetic field. The classical dynamics of the system is nonintegrable (and very similar to the standard map). We present results on this model for a quantum spin (i.e. for finite values of the spin lengthS). In particular we discuss the semiclassical regime,S1, using the concept of Wigner functions to define a suitable probability distribution. In regular regions of phase space the time evolution of the probability distribution shows an algebraic decay of correlations as in quantum mechanics. In chaotic regions of phase space it is characterised by a positive Lyapunov exponent which depends onS. In these regions semiclassical trajectories coincide with classical ones fort <₀ where ₀InS.     

Spectral duality for planar billiards

For a bounded open domain with connected complement inR ² and piecewise smooth boundary, we consider the Dirichlet Laplacian- on and the S-matrix on the complement ^c . We show that the on-shell S-matricesS _k have eigenvalues converging to 1 askk ₀ exactly when-- has an eigenvalue at energyk ₀ ² . This includes multiplicities, and proves a weak form of transparency atk=k ₀. We also show that stronger forms of transparency, such asS _{k 0} having an eigenvalue 1 are not expected to hold in general.     

The electrodynamics and statistical mechanics of linear plasma response functions

The purpose of this paper is to review and to extend, wherever possible, the Kramers-Kronig relations, sum rules, and symmetry properties for the electrodynamic transport tensors of a linear plasma medium. For complete generality, we consider both nonrelativistic and relativistic plasmas with and without external magnetic fields. Our study is carried out first within the framework of classical electrodynamics. We then exploit the statistical-mechanical fluctuation-dissipation theorem to further obtain the Onsager symmetry relations and Kubo sum-rule frequency moments. Of special significance is the emergence of a variety of new Kramers-Kronig formulae andf-sum rules for the inverse dispersion tensor.Nomenclature E(k,) electric field intensity - Ê(k,) electric field in absence of plasma particles, - (k,) electric field due to the plasma particles (=E-Ê) - B(k,) magnetic induction - D(k,) electric induction - H(k,) magnetic field strength - B ₀ constant external magnetic field - A ₀ vector potential corresponding toB ₀ - (k,),j(k, co) charge and current densities due to the plasma particles - (k,),J(k,) charge and current densities of the external agency - (k,,B ₀) dielectric tensor of the plasma medium in the presence of B₀ - (k,,B ₀) diamagnetic tensor - (k, co,B ₀) (k,,B ₀) – 1, electric polarizability tensor - (k,,B ₀) magnetic polarizability tensor - (k,,B ₀) ordinary conductivity tensor - (k,,B ₀) external conductivity tensor - D(k,,B ₀) n²T–(k,,B ₀), dispersion tensor, where T=1-kk is the transverse projection tensor (k being the unit vector in the direction ofk) andn = kc/ the index of refraction - n²T – 1, = vacuum wave operator (value of D in vacuum) - 1/2( + ), Hermitian part of - ^{^} 1/2( – ), Anti-Hermitian part of a - , real and imaginary parts of a - R(r,t) dissipated power per unit volume of plasma - U total energy absorbed by the plasma - R(k,) E^*(k,) · (k,,b ₀) ·E(k,) corresponding spectral energy density - W(r,t) 1/2₀E²(r, 0 + (l/2₀) B²(r,t), field energy density - W(k,) 1/2₀E^*k,) ·E(k,) + (l/2₀)B ^*(k,) · B(k,), energy content in a certain domain of (k,)-space for a single mode - x _i,p _i,v _i coordinate, momentum, and velocity of ith electron - _i [1–(_i ²/c²)]^–1/2 - X _j,P _j,V _j coordinate, momentum, and velocity of jth ion - {A _q}, {E_q} field coordinates and momenta - j_k(t),J _k(t) perturbations in the microscopic electron and ion current densities due to the presence of the small external vector potential agencyâ(r,t) = (1/L³) â_k(t) expi k ·r - Liouville distribution function = ⁰ + - ⁰ macrocanonical distribution function characterizing the equilibrium state of the system in the infinite past - small perturbation due toA - H⁰ Hamiltonian of equilibrium system which includes interaction - H Hamiltonian for the interaction between the system and the small external perturbing agencyA - ⁰ = d^R()⁰ expectation value of any quantity over the equilibrium ensemble (d^R is an element of hypervolume in -phase space) - G(12) two-particle distribution function - F(1) one-particle distribution function - g(¦x₂ – x₁ ¦) [G(12)/F(1)F(2)] – 1, pair correlation function - N total number of electron in volume L³ - n ₀ equilibrium density (of electrons) - ^–1 temperature (in energy units) - ₀ (n₀e²/m₀)^1/2, equilibrium electron plasma frequency - _c ¦e ¦–B ₀/m, electron frequency - ^–1 ( ₀/n₀e²)^1/2, Debye length - ₀ (n₀Ze²/M₀)^1/2, equilibrium ion plasma frequency - _c ZeB₀/M, ion cyclotron frequency     

Conditional stability of multiple-charged solitons

The stability of the three-dimensional multiple-charged soliton solutions to the nonlinear field equations is studied by Lyapunov's method. It is proved that an absolutely stable soliton solution can not exist in any field model. By imposing the subsidiary condition ^pQ_i=0 (fixation of charges) we find a sufficient condition for stability of the stationary soliton which includes the inequality ^{k i} (Q ⁱ / ^k <0. An illustrative example is considered.     

Abstract scattering theory

The asymptotic condition is formulated for a system whose theory is more general than quantum mechanics. Its logic forms an orthocomplemented weakly modular -lattice. The set of states , consisting of all the probability measures on , is endowed with the most suitable metric physically, called here the natural one. In this space it is proved that the asymptotic condition implies the existence of two convex automorphisms _+- of which we call the wave-automorphisms. From these theS-automorphism _– ^–1 ₊ is defined and corresponds to the scattering operator in conventional quantum theory.     

2- And 3-cochains in 4-dimensional SU(2) gauge theory

Explicit formulae are derived for the 2- and 3-cochains _uvq ⁽²⁾ (i, j, k) and _uvq ⁽²⁾ (i, j, k, ) in SU(2) gauge theory in 4 dimensions. It turns out that _uvq ⁽²⁾ (i, j, k, ) is given by the volume of a spherical tetrahedron spanned by the gauge transformations relating the gaugesi, j, k, l.     

Dielectric properties of titanium and gadolinium doped MgO single crystals

The dielectric properties of titanium doped magnesium oxide (Ti/MgO) and gadolinium doped magnesium oxide (Gd/MgO) single crystals have been measured at room temperature over the frequency range 500 Hz to 50 kHz. For both the crystals, the dielectric constant is found to be independent of frequency and the ac conductivity Re{_ae} agrees well with the relation Re{_ae} ⁿ , being the angular frequency with n=0.84±0.05 for Ti/MgO andn=0.81±0.03 for Gd/MgO. The data fits well with the relation ^n–1(n<1), being the dielectric loss factor. An explanation may be found on the basis of the hopping phenomenon.     

Cyclotron instabilities of a two-component electron plasma

A study is made of instability at frequencies close to the electron cyclotron frequency _B and its multiples, subject to the presence of two different groups of electrons. It is shown that a mixture of hot and cold electrons ( _ph ² _pc ² ) in the region of frequencies s _B, s2 can be unstable with respect to waves of the flute type (k _z=0) with maximum increment _max ( _ph/_pc). _B, if there exists an interval of transversal velocities in whichF/ >0. When the curvature of the magnetic field is taken into account, even waves with _B can be unstable in such a plasma. The effect of spatial inhomogeneity of the hot component on flute-type instability and on two-beam cyclotron instability is also examined.The author extends his thanks to A. B. Mikhajlovskij for his valuable comments and discussions.     

Contrast ratio and separation factor in multiphoton dissociation of supercooled UF6 irradiated with multifrequency 16 μm Raman-laser radiation

In infrared multiphoton dissociation of supercooled UF₆ irradiated with multifrequency para-H₂ Raman laser beams, separation factors and contrast ratios were measured by selective multiphoton ionization of the photoproduct UF₅ at 532 nm followed by time-of-flight mass spectrometric analysis. The relationship between separation factor and contrast ratio is discussed theoretically and quantitatively investigated in the experiments. From this relationship, we obtain the irradiation conditions of the laser-beam fluences for attaining a high separation factor and estimate the value of the intrinsic separation factor in multifrequency dissociation of UF₆.Abbreviations C _r (235) contrast ratio with respect to²³⁵UF₆ - _{q s5} yield of isotopically selective dissociation with respect to²³⁵UF₆ - _{q s8} yield of isotopically selective dissociation with respect to²³⁸UF₆ - _{q n5} yield of isotopically non-selective dissociation with respect to²³⁵UF₆ - _{q n8} yield of isotopically non-selective dissociation with respect to²³⁸UF₆ - S separation factor - S ₀ intrinsic separation factor - i fluence of individual beam i [J/cm²] - ₁ Raman-laser beam for exciting²³⁵UF₆ molecules selectively - ₂ Raman-laser beam for pumping UF₆ molecules excited by ₁ - ₃ Raman-laser beam for pumping excited UF₆ molecules further to a dissociative state     

High-frequency sum rules for the quasi-one-dimensional quantum plasma dielectric tensor

A high-frequency sum-rule expansion is derived for all elements of the spinless quasi-one-dimensional quantum plasma response tensor atT=0 K. As in the magnetized classical plasmas, we find that ₄ ¹³ is the only coefficient of ^–4 that has no correlational term. Further, we find that the correlations either enhance or reduce the negative quantum dispersion, depending on the direction of propagation. It is also noted that the quantum effect does not exist for the ordinary and the extraordinary modes for perpendicular and parallel propagation, respectively.     

Beam shear-Alfven instability in two-component tokamak

The authors consider from a theoretical standpoint the excitation of shear-Alfven waves in a tokamak in which the plasma contains a fast ion group. It is assumed that the fast ions are formed as a result of fast neutral atoms injected into the tokamak. An expression is derived for the growth rate of the shear-Alfven oscillations, with an arbitrary relationship between the transverse wave length and the dimension of the Larmor and drift orbits. The authors analyse the part played by the finite orbit effect in the case of a longitudinal beam with a small Maxwellian velocity spread and an arbitrary ratio between the directed velocityV ₀ and the Alfven velocityc _A . It is demonstrated that at a finite ratioV ₀/c _A two physically different types of oscillations may build up, corresponding to the two signs of the ratio/k _¦ ( is the oscillation frequency,k _¦ is the longitudinal wave number). The growth rate for perturbations with /k_¦<0 is greater than for /k>0.     

Dielectric properties of NaCl1−xBr and KCl1−xBrx mixed ionic solution

In the present paper a three-body potential model (TBPM) has been employed for the analysis of dielectric behaviour of NaCl-NaBr and and KCl-KBr mixed crystals with varying compositions. The physical properties like dielectric constants ( ₀ and ), optic mode frequencies ( _OLO and _TO), effective charge parameter (e _s ^* ), optic mode Grüneisen parameters and strain derivatives of ₀ and dielectric constants have been calculated. The results achieved in the present study are found in fairly good agreement with the available experimental data. The results obtained by previous investigators are also shown for the sake of comparison.     

Some properties of a collision term of a kinetic equation in a magnetic field

The collision term of a Fokker-Planck type kinetic equation is derived for the case of a two component magnetized plasma. It is shown that the collision processes are fully described by one symmetric two-dimensional dyadicQ. The collision term is modified for the case in which the distribution function of the field particles is Maxwellian.Conditions under which the magnetic Rosenbluth potentials can be introduced are studied. It is shown, in case that the distribution function of the field particles is Maxwellian, that the coefficients of friction and diffusion are expressible in terms of two scalar potentials only if _a = 0 or if the components D and D of the difusion coefficient are constant with respect to _a , for arbitrary _b of the field particles.     

Relations between Black Hole Spin and Angular Velocity of Accreting Particles near the Horizon

Evolution characters of angular velocity _H of a Kerr black hole (BH) and distribution characters of angular velocity _p of accreting particles near the BH horizon are investigated in the case of thin and thick disks, respectively. It is shown that _H evolves in a non-monotonous way in the case of thin-disk-pure-accretion, attaining a maximum at a _* 0.994. This evolution character turns out to depend on the radial gradient of _p near the BH horizon. It is proved that both quantities, ( d_H /dt) _ms and ( _p /r)_{r=r H}, vanish at the same value of a _*: a _*0.994, and an explanation for the non-monotonousness of _H is provided.     

Asymptotic behaviour of spin-momentum distribution observables for fermion fields with cut-off self-coupling

In a previous paper asymptotic creation and annhilation operatorsa _± ^# have been constructed by the Kato-Mugibayashi method from the creation and annihilation operatorsa ^# for spin 1/2 fields with an interaction Hamiltonian density which is an evendegree polynomial in the field with ultra-violet cut-off and its derivatives. For any eigenvector of the total HamiltonianH=H ₀+H _I partial isometries _± have been defined so thata _± ^# equal _± a ^# *_± on the ranges _± of _±. Since the existence of a groundstate ofH has been proved, the existence of at least one pair _± follows. The purpose of this paper is to show that for any _± orthogonal to the distribution of spins and momenta of the interacting Schrödinger states exp[–itH]_± approaches fort the distributions of spins and momenta of the free state exp[–itH ₀] if a wave-amplitude renormalization is carried out in _±. This is achieved by studying the expectation values of the operators in themaximally abelian W*-algebra generated by operators of the form a*a, in terms of whichany information about spins and momenta can be expressed.Supported in part by the National Research Council of Canada.     

Betatron-synchrotron resonance in free electron laser

In terms of Bogoliubov's nonlinear theory, the first five betatron-synchrotron resonances of _s=(p q)2K, p/q=1/2, 1, 3/2, 1/3, 2/3 which may occur during laser satulation establishing process have been generally examined. Contrast to previous studies we found that the most dangerous resonance does not take place in the vicinity of _s=2k, but in that of _s=k. The width of region of _s=k is proportional to with (k _w ² /k) remittance, the passing time over the region due to the laser field being amplified is only one pass over the undulator at most and depends on the gain, and the increment of synchrotron amplitude in passing time is proportional to .In summary we conclude that the betatron-synchrotron resonances do not have any significant effect for detrapping off-axis electrons in a practical case.     

A generalization of Dyson's formula

We give an integral representation for tempered distributions which have more general support properties inx space, than those usually assumed in the derivation of the Dyson formula.The existence of such an integral representation is shown to be equivalent to that of a suitable extension of an analytic function: namely, given an analytic function on a section of a domain of holomorphy extend it to imposing on it some growth conditions. L ² space methods ofL. Hörmander are used to solve this problem of extension. In order to apply these Hilbert space techniques, it was necessary to prove two important theorems on the growth of analytic function.From the physical point of view the formula we obtained is an integral representation for the commutator of two quasi local fields.     

Results from the First Year of Observations with the Wilkinson Microwave Anisotropy Probe

The Wilkinson Microwave Anisotropy Probe (WMAP) has produced all-sky maps in five frequency bands between 23 and 94 GHz that can be used to study the CMB. We present an overview of the results from an analysis of maps made with one year of data. The highlights are that a) the flat CDM model fits the data remarkably well, an Einstein-deSitter model (_tot = 1, =0) does not; b) from the polarization of the CMB there is evidence of the birth of the first generation of stars at z _r 20; c) when the WMAP data are combined and compared with other cosmological probes a cosmic consistency emerges: multiple different lines of inquiry lead to the same results. The best-fit flat cosmological model to just the WMAP CMB data shows that the matter density is _m h ² = 0.14 _–0.02 ^+0.02, the baryon density is _b h ² = 0.024 ± 0.001, and n _s = 0.99 ± 0.04. WMAP continues to operate, and so results will improve.