Bremsstrahlung from collisions of low-energy electrons with positive ions in a magnetic field

Bremsstrahlung from electron-ion collisions in a magnetic field is studied for low energies at which the Larmor radius of an electron is smaller than the characteristic impact parameter of close collisions in zero magnetic field. It is shown that the magnetic field does not qualitatively change the bremsstrahlung power at low frequencies smaller than the reciprocal time of electron transit in the vicinity of an ion in close collision in zero magnetic field. At high frequencies, the radiation intensity decreases in accordance with a power law, attains its minimal value, and then increases in accordance with a power law up to frequencies on the order of the electron cyclotron frequency. At such frequencies, the spectral power attains typical power values in zero magnetic field. At frequencies lower than the cyclotron frequency considered here, bremsstrahlung is polarized predominantly linearly in the plane formed by the magnetic field and the direction of radiation.     

Scattering of Low-Energy Electrons by Positive Ions in a Magnetic Field. I. Quantum Calculation of Transition Probabilities

We analyze electron–ion collisions in a magnetic field at a low temperature, for which the electron’s Larmor radius is less than the characteristic impact parameter of close collisions without the magnetic field. This ratio of spatial scales is realized in the photospheres of magnetic white dwarfs and in the experiments of antihydrogen creation. Under considered conditions, an electron transits from the initial to the final state via an intermediate quasibound state. We put forward an approximate analytical procedure for the quantum-mechanical calculation of the probabilities for an electron to transit between Landau levels due to a collision with an ion. We reduce the calculation to the inversion of finite-dimension matrices. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 6, pp. 512–525, June 2008.     

Electron-phonon drag in degenerate conductors in a magnetic field

Mutual drag of electrons and phonons in degenerate conductors in classical magnetic fields is considered. It is shown that the coupled kinetic equations for nonequilibrium electron and phonon distribution functions can be transformed into a system of Volterra’s inhomogeneous integral equations. A solution is found to the system of integral equations with inclusion of all terms yielding contributions linear in the degeneracy parameter. An analysis is made of the effect of a magnetic field on momentum relaxation in an electron-phonon system.     

Scattering of low-energy electrons by positive ions in a magnetic field. II. Resonances,transition probabilities,and transport frequencies

We analyze quantum-mechanically electron-ion collisions in a magnetic field at a low temperature, for which the electron's thermal energy is less than the energy gap between two Landau levels and the electron's Larmor radius is less than the characteristic impact parameter of close collisions without the magnetic field. To calculate transition probabilities, we use the analytical procedure proposed in the first part of our paper. We calculate the energy and lifetime of the resonant (autoionization) states of an electron embedded in the Coulomb electric field of an ion and in a uniform magnetic field. The obtained values coincide in order of magnitude with the known exact numerical values. We find that the electron backward scattering probability irregularly (chaotically) depends on the particle energy and the magnetic field. We propose analytical approximations for the collision transport frequencies, one of which describes the electron braking along the magnetic field and another, equalizing of the temperatures corresponding to the electron motion along and across the magnetic field. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 8, pp. 682–699, August 2008.     

Resistive Electrostatic Ion Cyclotron Instability in Plasmas

The stability of electrostatic ion cyclotron waves propagating obliquely with respect to the background magnetic field is studied for collisional, fully-ionized plasmas in which there is a relative field-aligned streaming between electrons and ions. It is found that electron-ion collisions, in conjunction with electron streaming, provides a mechanism for instability. The role of electron streaming is to supply a source of free energy and the role of electron-ion collisions is to restrict the field-aligned mobility of the electrons, thus preventing them from establishing a Boltzmann equilibrium. Ion-ion collisions and finite ion Larmor radius are found to exert a stabilizing influence. The instability is analyzed for both current-carrying plasmas and counterstreaming-beam-plasma systems.     

Die Methode der Normallösungen für die Vlasov-BGK-Gleichung

The linearized Vlasov equation with collision damping is solved by the method of normal modes of Van Kampen and Case. The system considered is an infinitely extended nonrelativistic nondegenerate electron gas with neutralizing ion background and neutral particles. There is no magnetic field. Collision damping is taken into account by complete Bhatnagar-Gross-Krook collision integrals for electron-electron collisions and electronion collisions; in the case of a partially ionized gas elastic collisions between electrons and neutrals can be included likewise. The Vlasov-BGK operator is transformed into an integral operator yielding complex singular normal modes even if the equilibrium distribution is a Maxwellian. The adjoint integral equation belongs to a more complicated type than that of a collision-free system. Its solutions must be orthogonalized. The set of all normal modes is complete rendering the exact solution of the initial value problem possible. The completeness is shown by transformations and regularization of the singular integral equation of the initial value problem, the techniques of Case not being applicable because of the complicated type of this equation.     

Synchronization,zero-resistance states and rotating Wigner crystal

We show, in a framework of a classical nonequilibrium model, that rotational angles of electrons moving in two dimensions (2D) in a perpendicular magnetic field can be synchronized by an external microwave field whose frequency is close to the Larmor frequency. The synchronization eliminates collisions between electrons and thus creates a regime with zero diffusion corresponding to the zero-resistance states observed in experiments with high mobility 2D electron gas (2DEG). For long range Coulomb interactions electrons form a rotating hexagonal Wigner crystal. Possible relevance of this effect of synchronization-induced self-assembly for planetary rings is discussed.     

On the theory of surface impedance of metals placed in a magnetic field

The smooth non-monotonous dependence of the metal surface impedance upon the magnetic field H is investigated theoretically for the cases of diffuse and specular reflection of electrons from the specimen boundary. The type of the electron-surface interaction has been found to have very little effect on the magnitude of the impedance Z_α(H) in the range of weak magnetic fields [equation (1)]. In a strong field [equation (2)] the surface impedance behaves differently for diffuse and specular reflection. The form of the Z_α(H) function depends essentially on the ratio of the electromagnetic wave frequency ω and the collision frequency of electrons ν. This provides a possibility of establishing experimentally the frequency of electron collisions with volume scatterers.     

Electromagnetic radiation from positive-energy bound electrons in the Coulomb field of a nucleus at rest in a strong uniform magnetic field

A classical analysis is presented of the electromagnetic radiation emitted by positive-energy electrons performing bound motion in the Coulomb field of a nucleus at rest in a strong uniform magnetic field. Bounded trajectories exist and span a wide range of velocity directions near the nucleus (compared to free trajectories with similar energies) when the electron Larmor radius is smaller than the distance at which the electron-nucleus Coulomb interaction energy is equal to the mechanical energy of an electron. The required conditions occur in magnetic white dwarf photospheres and have been achieved in experiments on production of antihydrogen. Under these conditions, the radiant power per unit volume emitted by positive-energy bound electrons is much higher than the analogous characteristic of bremsstrahlung (in particular, in thermal equilibrium) at frequencies that are below the electron cyclotron frequency but higher than the inverse transit time through the interaction region in a close collision in the absence of a magnetic field. The quantum energy discreteness of positive-energy bound states restricts the radiation from an ensemble of bound electrons (e.g., in thermal equilibrium) to nonoverlapping spectral lines, while continuum radiative transfer is dominated by linearly polarized bremsstrahlung.     

Diffusion in a collisional standard map

Test particle evaluation of the diffusion coefficient in the presence of magnetic field fluctuations and binary collisions is presented. Chaotic magnetic field lines originate from resonant magnetic perturbations (RMPs). To lowest order, charged particles follow magnetic field lines. Drifts and interaction (collisions) with other particles decorrelate particles from the magnetic field lines. We model the binary collision process by a constant collision frequency. The magnetic field configuration including perturbations on the integrable Hamiltonian part is such that the single particle motion can be followed by a collisional version of a Chirikov-Taylor (standard) map. Frequent collisions are allowed for. Scaling of the diffusion beyond the quasilinear and subdiffusive behaviour is investigated in dependence on the strength of the magnetic perturbations and the collision frequency. The appearance of the so called Rechester-Rosenbluth regime is verified. It is further shown that the so called Kadomtsev-Pogutse diffusion coefficient is the strong collisional limit of the Rechester-Rosenbluth formula. The theoretical estimates are supplemented by numerical simulations.     

Zur Theorie der Rückstreuung

Electrons emitted from a cathode, are partially backscattered to the cathode surface by collisions with gas molecules. No equilibrium between electrons, gas and field is presumed for a theoretical treatment of this process, in contrary to the conception of Thomson [1]; instead of it the effect of single collisions is investigated assuming isotropy of scattering. The collision numbers, which may be calculated from successive integral transforms, are shown to form a monotone decreasing sequence. In the field-free case the collision numbers and the back diffusion rates for the first collisions may be explicitely stated; the convergence of this method is rather poor, however. A model for back diffusion in an electric field, whereby the effect of primary collisions only is considered, is completely treatable. The results depend on the angular and energy-distribution of the emitted electrons. A comparison with other formulas and with experimental results for back scattering shows a better agreement between the latter and our equations than in the case of the Thomson-Loeb relation. The consequences on the theory of cathode fall are briefly discussed.     

Testing the chiral magnetic effect with central U+U collisions

A quark interaction with topologically nontrivial gluonic fields, instantons and sphalerons, violates P and CP symmetry. In the strong magnetic field of a noncentral nuclear collision such interactions lead to the charge separation along the magnetic field, the so-called chiral magnetic effect (CME). Recent results from the STAR collaboration on charge dependent correlations are consistent with theoretical expectations for CME but may have contributions from other effects, which prevents definitive interpretation of the data. Here I propose to use central body-body U+U collisions to disentangle correlations due to CME from possible background correlations due to elliptic flow. Further, more quantitative studies can be performed with collision of isobaric beams.     

Diffusion of charged particles in strong large-scale random and regular magnetic fields

The nonlinear collision integral for the Green’s function averaged over a random magnetic field is transformed using an iteration procedure taking account of the strong random scattering of particles on the correlation length of the random magnetic field. Under this transformation the regular magnetic field is assumed to be uniform at distances of the order of the correlation length. The single-particle Green’s functions of the scattered particles in the presence of a regular magnetic field are investigated. The transport coefficients are calculated taking account of the broadening of the cyclotron and Cherenkov resonances as a result of strong random scattering. The mean-free path lengths parallel and perpendicular to the regular magnetic field are found for a power-law spectrum of the random field. The analytical results obtained are compared with the experimental data on the transport ranges of solar and galactic cosmic rays in the interplanetary magnetic field. As a result, the conditions for the propagation of cosmic rays in the interplanetary space and a more accurate idea of the structure of the interplanetary magnetic field are determined.     

Cyclotron mechanism of electron acceleration in subpicosecond laser plasma

The effect of ultrastrong magnetic fields generated in a relativistic-intensity subpicosecond laser plasma on the acceleration of fast electrons was studied. It is shown that resonance electrons can continuously accumulate energy from the circularly polarized laser field in the presence of a longitudinal magnetic field. For the linear polarization and a transverse magnetic field, energy accumulation has a pulse-periodic character, and the electron trajectories correspond to electron rotation in the Larmor orbit in a quasi-stationary magnetic field, while the energy strongly oscillates. In both cases, electron energy may attain values higher than 100 MeV for intensities of 10²⁰ W/cm².     

Current-Driven Kink-Like Instability in Collisional Plasmas

The stability of left-hand circularly polarized waves propagating along an external magnetic field with wavelengths much larger than the ion Larmor radius is studied for fully-ionized collisional plasmas carrying a field-aligned current. It is found that, in the presence of electron-ion collisions, this "kink-like" instability has two branches of unstable wavenumbers: a main branch and a resistive branch. The resistive branch owes its existence to electron-ion collisions, but its growth rate is much smaller than that of the main branch, which is typically some fraction of the ion cyclotron frequency. The effect of collisions on the main branch is to reduce its maximum growth rate while extending the range of unstable wavenumbers to larger values. However, these changes are significant only when the electron-ion collision frequency is comparable to the electron cyclotron frequency. The dispersion relation is solved numerically for plasma and magnetic field parameters appropriate to the UCLA arcjet plasma. The results show that, within the framework of an infinite and homogeneous theory, the kink-like instability should occur in this plasma device.     

负氢离子源中电子能量沉积三维数值模拟研究

本文理论计算了多峰离子源永磁体, 采用二体碰撞模型(binary collision)处理电子之间的库仑碰撞, 采用空碰撞(null-collision)方法处理电子与氢元素相关粒子, 开发了全三维PIC-MCC模拟算法, 并利用该算法模拟了多峰离子源中电子沉积过程, 分析了多峰磁场对电子的空间和能量分布影响, 结果显示: 电子的非均匀分布起源于高能电子在引出区的B× ▽B漂移.     

Two-body collisions and time dependent Hartree-Fock theory

The time-dependent Hartree-Fock (TDHF) theory is generalized in order to include the effect of two-body collisions (i.e. the residual interaction). This is achieved by adding a collision integral into the TDHF equations, similar to the one ordinarily used in the Boltzmann equation. It is shown, that two-body collisions arise from the imaginary part of the effective interaction between two nucleons whereas the Hartree-Fock field is associated to the real part of the same interaction. There is thus no double counting when the collisions are added to a single particle field. Various approximations for the collision integral are discussed and their accuracy evaluated. Special effort is made in order to obtain conserving approximations. It is shown that for discrete fields, energy as well as momentum conservation is achieved by off-shell scattering processes. In the light of a previous paper, it is argued that two-body collisions should dominate the irreversible processes above some critical energy (roughly 200 MeV per nucleon). Below this energy the irreversible effects due to the single particle field and the collisions are expected to be of the same order of magnitude.     

Completely bound motion of a positive-energy electron in the coulomb field of a motionless nucleus and a uniform magnetic field

We show that the completely bound classical motion of a positive-energy electron is realized in the Coulomb field of a motionless nucleus and a uniform magnetic field. Such a motion exists due to conservation of the so-called invariant tori in the phase space of the system for not only the negative, but also for the positive energy of an electron. The completely bound trajectories occupy a much larger interval of the velocity directions compared with free trajectories for the same energy in a range of distances from the nucleus in which the typical time of the electron transit near the nucleus is larger than the cyclotron-gyration period, while the negative energy of Coulomb interaction is larger (in absolute value) than the total electron energy. The indicated range of distances is realized in the case of a low electron energy or a strong magnetic field when the Larmor radius of the electron is smaller than the characteristic impact parameter of the close Coulomb collisions in the absence of a magnetic field. The required conditions are realized in the photospheres of isolated magnetic white dwarfs and in the experiments on creation of antihydrogen.     

Effect of electron-neutral collisions on the satellites of the Thomson scattering spectrum in arc plasmas

The effect of electron-neutral collisions on the high frequency spectrum of laser radiation scattered by the free electrons of a plasma is investigated for a partially ionized H₂ are plasma at atmospheric pressure. The calculations are carried out along Gorog's theory solving the linearized Boltzmann equation for electrons with a collision term. The collision integral is approximated by a Krook relaxation model with the collision frequency determined from experimental electron-atom scattering data. The collisions influence size, half width, and position of the high frequency satellites. In a H₂ arc plasma, the change of the satellites' position is negligible as well as the change in half width within experimentally attainable error limits. The change of size is of minor importance, since the general evaluation procedure uses only normalized scattering intensities. Thus, for laser scattering experiments in are plasmas the collision-free theory can be applied.     

横向磁场对辉光等离子体阴极区电子输运过程的影响

本文动用改进的蒙特卡罗技术，研究了横向磁场对氦气直流辉光放电阴极区电子输运过程的影响。