New critical current of ionization waves in an axial magnetic field

The upper critical current for the occurrence of ionization waves in an axial magnetic field is found in the positive column of rare-gas discharges. As the field is increased, the critical current slightly increases from the Pupp value, and after passing the maximum, finally becomes very small.     

Dynamics of magnetic insulation failure and self-organization of an electron flow in a magnetron diode

The dynamics of back cathode bombardment (BCB) instability in a magnetron diode (a coaxial diode in a magnetic field, B ≡ B _0z ≡ B ₀) is numerically simulated. The quasi-stationary regime of electron leakage across the high magnetic field (B ₀/B _cr > 1.1, where B _cr is the insulation critical field) is realized. An electron beam in the electrode gap is split into a series of bunches in the azimuthal direction and generates the electric field component E _θ(r, θ, t), which accelerates some of the electrons. Having gained an extra energy, these electrons bombard the cathode, causing secondary electron emission. The rest of the electrons lose kinetic energy and move toward the anode. Instability is sustained if the primary emission from the cathode is low and the secondary emission coefficient k _se=I _se/I _{e, BCB} is greater than unity. The results of numerical simulation are shown to agree well with experimental data. A physical model of back-bombardment instability is suggested. Collective oscillations of charged flows take place in the gap with crossed electric and magnetic fields (E × B field) when the electrons and E × B field exchange momentum and energy. The self-generation and self-organization of flows are due to secondary electron emission from the cathode.     

Two Components of the Total Ionization Cross Sections of Atoms and Molecules by Electron Impact: Resonant Excitation and Decay of the Fermi Electron-Hole System and the Dipole Electron Transition from a Bound to a Free State at a Binary Collision

Large volume of the experimental data on the ionization cross sections of atoms and molecules by electron impact obtained by various authors using different methods is analyzed. The dependence of the ionization cross section Q on the energy of the incident electron E is described by a curve with a maximum. For E I, where I is the ionization potential, the cross section naturally vanishes. For E > I, it first increases fast, passes through a high maximum, and then monotonically decreases with increasing E. For comparatively large energies E > 100 I, the Bethe formula describes the experimental data almost exactly, but in the region of maximum I < E < 10 I, it deviates significantly from the measurement data. In the present paper it has been established that the experimental dependence Q(E) in the region of maximum is well described by a resonant curve similar to Lorentz distribution. It is assumed that the main contribution to the atomic ionization by a slow electron comes from the resonant excitation and the decay of the Fermi electron-hole system. An empirical formula for the cross section of atom ionization by electron impact Q(E) is suggested which takes into account resonance for incident electrons of small energies and is transformed into the Bethe formula for large E. The parameters of the formula for the ionization cross section are calculated by the least-squares method for H, He, Ne, Ar, C, N, O, Li, Na, H₂, N₂, O₂, K-shells of C, N, Ne, Ar, K, Ca, Rb, and Sr atoms and molecules. A comparison of the experimental dependences of the ionization cross section on the energy of the incident electron with the Bethe theoretical formula and empirical formulas suggested by Lotz, Alkhazov, Kim and Rudd, and Povyshev et al. demonstrates that the formula suggested in the present paper describes the available experimental data better than others.     

Manipulating the magnetoimpedance by dc bias current in amorphous microwire

We have studied the effect of the internal circumferential magnetic field H_B created by the dc bias current I_B on longitudinal and off-diagonal magnetoimpedance (MI) in amorphous microwire with helical anisotropy and experimentally demonstrated that by changing the dc current I_B it is possible to considerably change the MI dependencies. The bias current applied to such microwire transforms the symmetric and hysteretic MI curve to asymmetrical and anhysteretic. The minimum of longitudinal MI curve shifts from the zero-field point. Reversing the bias current causes reversal of the bias field direction and results in a mirroring of the MI curves. It is proposed to apply a cross-checking of two MI curves with I_B of different polarity for magnetic field sensing. In particular, this method allows to overcome the drawbacks usually associated with longitudinal MI—namely the impossibility to determine the direction of an external axial magnetic field H_E and the low sensitivity near the zero-field point. Moreover, the operating range of the longitudinal MI sensor, in contrast to the off-diagonal one, can be much extended as it exhibits a quite high sensitivity in the field range up to one order of magnitude higher than the anisotropy field.     

Effect of an electric field on the I–V curves of DyBa2Cu3−x Oy/1 wt % Pt HTSC ceramics

This paper reports on an experimental study of the effect of a magnetic field, B≤70 G, and an electric field, E=120 MV/m, on the critical current I _c and I–V curves of DyBa₂Cu_3?x O_y HTSC ceramics (x=0 and 0.2), both undoped and doped with 1 wt % Pt. It has been established that, in stoichiometric ceramics (x=0) at 77 K, I _c drops sharply (by more than an order of magnitude) already at very low B<1 G. In copper-deficient ceramics (x=0.2), I _c decreases with increasing B slowly, with Pt-doped samples exhibiting [on the dropping I _c (B) dependence] a peak effect, i.e., an increase rather than decrease of I _c at B≈10 G. As for the effect of an electric field on I _c and the I–V curves (the E effect), it is not observed in ceramics of a stoichiometric composition. DyBa₂Cu_2.8O _y samples acted upon by an electric field reveal a substantial increase in I _c and a decrease in the resistance R for I>I _c . In the case of DyBa₂Cu_2.8O_y/Pt, the electric field practically does not affect I _c but R decreases for I>I _c . In a sample placed in a magnetic field, the magnitude of the E effect is observed to correlate with the I _c (B) dependence. In particular, in Pt-doped samples, the E effect decreases with increasing magnetic field B not gradually but with a maximum appearing at B ≈10 G, i.e., in the region of the peak effect in the I _c (B) dependence. The data obtained suggest the conclusion that the electric-field effect in ceramics exhibiting weak links of the superconductor-insulator-superconductor (SIS) type correlates with magnetic vortex pinning.     

Numerical investigation of the theta pinch in intrinsic indiumantimonide

The electron-hole plasma in intrinsic InSb at 300 K can be compressed by electric and magnetic fields. In the theta-pinch configuration one applies, by a capacitor discharge over a one-winding coil around the sample, a magnetic field (0, 0,B _z), which induces an electric field (0,E _φ, 0); both fields cause the ambipolar motion (v _r, 0, 0) of the plasma. We describe the electron-hole plasma by means of a magnetohydrodynamical two-fluid model. The resulting system of differential equations is solved numerically under the assumptions of scalar hydrodynamic pressure and field-independent mobilities. The influence of the plasma properties on the theta pinch is studied as well as the dependence on the experimental conditions like radius of the sample, maximum value and risetime of the magnetic field.     

Radial Electric Field Shear Due to Neoclassical Effects in Transport Barriers

The E _r×B flow shear is simulated with a fully kinetic five-dimensional neoclassical Monte Carlo simulation for JET and ASDEX Upgrade plasma edge conditions. Here, E _r is the radial electric field and B is the magnetic field. It is shown that high enough shear for turbulence suppression can be driven at the Low (L) to High (H) transition conditions by pure neoclassical effects including ion orbit losses. Simulations indicate higher threshold shear for ASDEX Upgrade than for JET. Shear values are compared to different models and experimental results of critical shear, and isotope effect on shear is discussed. Formation of an internal transport barrier in FT-2 in the presence of lower hybrid waves is also studied.     

Excitation-autoionization cross sections and rate coefficients for Ga-like ions

Detailed level-by-level calculations of cross sections and rate coefficients for electron impact direct and indirect ionization of ions belonging to the GaI isoelectronic sequence (ground 3d ¹⁰4s ²4p) have been performed. The cross sections are presented in the energy range near the threshold for the five ions Kr⁵⁺, Mo¹¹⁺, Xe²³⁺, Pr²⁸⁺ and Dy³⁵⁺. The rate coefficients are given for ions from Kr⁵⁺ to U⁶¹⁺ in the GaI sequence at seven electron temperatures (kT _e = 0.1E _I , 0.3E _I , 0.5E _I , 0.7E _I ,E _I , 2E _I and 10E _I , where E _I is the first ionization energy). The calculations include the contribution of direct ionization (DI) calculated using the Lotz formula approximation and the contributions of excitation-autoionization (EA) computed in the framework of the distorted wave (DW) approximation for the 4s-nl, 3d-nl and 3p-nl resonant inner-shell excitations. The ionization enhancement due to the EA channels is presented as a function of Z along the GaI isoelectronic sequence. The present results show the great importance of the EA processes; an ionization enhancement factor of up to 10 is predicted for instance for La²⁶⁺ (Z = 57) at electron temperature of coronal equilibrium maximum abundance.     

Magnetisch erregte ‚Seilwellen’︁ auf der kontrahierten Säule einer Argon-Mitteldruckentladung

The influence of a transverse magnetic field on a contracted argon discharge column (p = 23 torrs; I_discharge = 100…?200 ma) is investigated. The experiments show oscillatory behaviour of the column similar to rope waves, which becomes irregular with higher B-field intensities. The results of spectral and correlation measurements are discussed in relation to the corresponding non-linear wave equation qualitatively.     

NMR-ON measurements of123, 124, 131I in nickel

The magnetic hyperfine splitting frequencies of¹²³INi,¹²⁴INi and¹³¹INi in a zero external magnetic field have been determined by the NMR-ON method as 258.9(1), 165.9(1) and 179.5(2) MHz, respectively. With the known values of the magnetic moments, the magnetic hyperfine fields have been deduced:B _HF(¹²³INi)=30.17(5) T,B _HF(¹²⁴INi)=30.14(9) T,B _HF(¹³¹INi)=30.06(4) T; the weighted average isB _HF(INi)=30.11(4) T. The small difference of theB _HF(¹³¹INi) with those of¹²³INi and¹²⁴INi is discussed comparing with results of the hyperfine splitting frequency of iodine in iron host.     

Ionization wave as an Instability — Evolution and Nonlinear Effect

Evolution from the linear growth to the nonlinearly saturated state of ionization waves (moving striations) is investigated from a viewpoint of an instability which appears in a plasma. The experiments were performed observing backward waves excited below the upper critical current I_c in xenon, argon, and argon-mercury gases at pressures of the order of Torr. It is found that (1) the behavior of the evolution obeys the Landau amplitude equation; (2) the saturated amplitude does not depend on an initial value, but only on plasma parameters; (3) the linear growth and squared saturation level are proportional to the excess over I_c, and when frequency-controlled, they have a parabolic dependence on the frequency; and (4) nonuniform axial changes in the dc state due to the nonlinear effects appear in a form of enhanced ionization in the plasma where the electron temperature and density are increased. The way of these behavior can be applied to a large number of spatially or temporally unstable modes.     

Excitons and linear optical spectra of E33 and E44 in single wall carbon nanotubes under axial magnetic field

The E₃₃ and E₄₄ optical spectra of semiconducting single-walled carbon nanotubes under axial magnetic field (B) are studied using the tight-binding model, which also takes into account the exciton effect. It is found that the E₃₃ and E₄₄ splitting, induced by the axial magnetic field, is line increased with magnetic field, which can be described by the splitting rate. Also by investigation of the dependence of splitting rate, we found that it shows a clear (2n+m) family behavior besides the diameter dependence, which can be used as a supplemental tool to identify the tubes used in the experiment, and is expected to be detected by the future experiment.     

Anfachung und Dämpfung von Ionisationswellen in MHD-Kanälen und ihr Einfluß auf die effektive elektrische Leitfähigkeit,den effektiven Hall-Parameter und die mittlere Elektronentemperatur

The phase velocity, the amplification rate and the critical Hall parameter are theoretically determined for ionization waves in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both the magnetic field and the stream velocity. The investigations hold for seeded rare gases at any degree of seed ionization. The critical Hall parameter β_c depends on the degree of ionization, the ionization energy and the temperatures of electron gas T₀ and neutral gas T_g · β_c is always greater than one, if 0 < T₀ — T_g ? T₀ holds. The three-dimensional treatment indicates the existence of waves with a nonvanishing wave vector component in the direction of the magnetic field. The influence of ionization waves on mean current density, mean Hall field intensity and mean electron temperature is determined up to second order terms in the relative fluctuations of the electron temperature. The amplification of ionization waves reduces the effective electric conductivity, the effective Hall parameter and the mean electron temperature compared to the undisturbed state. Similar results are also obtained for steady state homogeneous isotropic turbulence and a special case of axially symmetric turbulence. Furthermore, a component of the electric field in direction or in opposite direction to the magnetic field vector may be generated by non isotropic and non homogeneous turbulence.     

Pinning of pancake vortices in a three-dimensional Josephson medium and structure of the vortex lattice in the “critical” state

A system of pancake vortices formed near the boundary of a sample in a monotonically increasing external magnetic field is calculated with allowance for pinning due to the cellular structure of the medium for various values of the pinning parameter I, which is proportional to the critical current of the junction and the cell diameter. The shortest distance from the outermost vortex to the nearest neighbor is proportional to I ⁻¹¹. It is shown that the pinning parameter has a critical value I _c separating two regimes with different types of critical states. For I<I _c the external magnetic field has a threshold value H _t(I), above which the field immediately penetrates the interior of the junction to an infinite distance. For I>I _c the magnetic field decays linearly from the boundary into the interior of the junction. The value obtained in the study, I _c=3.369, differs from the value of 0.9716 postulated by other authors. The dependence of the slope of the magnetic field profile near the boundary on I is determined. It is shown that the slope is independent of I in intervals 2πk<I<2πk+π. Fiz. Tverd. Tela (St. Petersburg) 39, 1958–1963 (November 1997)     

Self-consistent equilibria in a cylindrical reversed-field pinch

Summary A previous investigation by one of us, concerning the self-consistent equilibria of a two-region (plasma+gas) cylindrical Tokamak, is extended to the similar equilibria of a Reversed-Field Pinch, where a significant current density is driven by a dynamo electric field due to turbulence. The previous model has been generalized under the following basic assumptions:a) to the lowest order, the turbulent dynamo electric fieldE ^t is expressed as a homogeneous function of degree 1 of the magnetic fieldB, sayE ^t =α·B, with α being a 2nd-rank tensor, homogeneous of degree 0 inB, and generally depending on the plasma state;b)E ^t does not appear in the plasma power balance, as if it were produced by a Maxwell demon able to extract the needed power from the plasma internal energy. In particular we show that, in the simplest case when both α and the plasma resistivity η are isotropic and constant, the magnetic field turns out force-free with constant abnormality αμ₀/η for vanishing axial electric fieldE _z . This case has also been solved analytically, for whateverE _z , under circular, besides cylindrical, symmetry.     

Evolution of electron-hole avalanches and streamers in indirect gap semiconductors

A numerical simulation of the origination and evolution of streamers in semiconductors has been performed using the diffusion-drift approximation including the impact and tunnel ionization. It is assumed that an external electric field E ₀ is static and uniform, an avalanche and a streamer are axisymmetric, background electrons and holes are absent, and all their kinetic coefficients are identical. The linear evolution of an electron-hole avalanche, an avalanche-to-streamer transition, and two successive stages of the evolution of the streamer—intermediate “diffusion” and main exponentially self-similar—have been examined in detail. It has been shown that a streamer is similar to a dumbbell with conical weights. The bases of these cones, streamer fronts, are thin shells, which contain almost the entire streamer charge and are close in shape to the halves of ellipsoids of revolution. A front propagates so that its shape and the shape of the weight of the dumbbell, the maximum field on the front, and the electron-hole plasma density in weights remain unchanged. The field strength behind the front is much smaller than E ₀, but increases with approaching the bar of the dumbbell whose diameter increases with the time t owing to the transverse diffusion. The electron and hole densities in the bar increase due to the impact ionization in an almost uniform field, which is only slightly lower than E ₀. At the diffusion stage, the length of the streamer and the curvature radius of its front increase with constant rates, which are determined not only by the impact ionization and drift, but also by diffusion. In relatively low fields (E ₀ ≲ 0.4 MV/cm for silicon) this stage ends due to the appearance of the instability of the front. In higher fields, the tunnel ionization is manifested before the appearance of instability and gives rise to the appearance of a new-type streamer. Its main feature is the stable exponential increase in all spatial scales with the same response time t _R , so that the charge-carrier density and field strength at large times t depend only on one vector variable $ \hat R $ \hat R = Rexp(−t/t _R ). This means that the solution of a Cauchy problem describing the evolution of the streamer in the uniform field is asymptotically exponentially self-similar.     

Calculation of magnetic field in the region of the superconducting winding of window frame dipole for particle accelerators

The necessity of simulations in design of superconducting dipole magnets is due to the following circumstances. First, the critical current as a function of the magnetic field I _c(B) for the multicore superconducting cable which drops strongly requires the knowledge of the value of maximum magnetic field “felt” by its coils for estimation of the working current of the magnet. Second, for choosing the optimal number of coils of the winding (1 or 2) and the working current of the magnet, the ratio of B _max for the inner and outer layers of the dipole magnet winding should be known. Since usually the length of the dipole magnet exceeds many times its transverse size, in this work all calculations of B(x, y) are performed in the transverse plane crossing the center of the magnet. The field at the central point is chosen to be B(0, 0) = 2 T (this is the characteristic working value close to the maximum value in the dipole magnet of this type). In this work, the results of calculation of B(x, y) for single-and double-layered windings with 8 and 16 coils from circular hollow cable are presented.     

Penetration of magnetic field into a long periodically modulated Josephson contact

A new approach to magnetic field profiling inside a Josephson contact is suggested. Its essence consists in analyzing continuous variation of a current configuration leading to a decrease in the Gibbs potential. With this approach, one can find a configuration into which the Meissner state turns when an external field slightly exceeds the upper boundary of the Meissner regime and trace the evolution of this configuration with increasing field. Calculations show that there exists critical value I _c of the pinning parameter in the range 0.95–1.00. This critical value separates two possible conditions of magnetic field penetration into the contact. At I > I _c, a near-boundary current configuration completely compensating for the external field inside the contact arises irrespective of the external field strength. At I < I _c, such a situation is observed only until the external field strength exceeds certain value H _max. Higher fields penetrate into the contact indefinitely deep. In nearboundary configurations, the magnetic field drops with increasing depth almost linearly. Its slope k has rational values, which remain constant within finite intervals of I. As I goes beyond a given interval, k rises stepwise and takes on another rational value. When an external magnetic field is switched on adiabatically, configurations with a maximal growth rate of the magnetic field are observed.     

Mode Transition of Ionization Waves in Non-Uniform Magnetic Field

Experimental observations on mode transition in a positive column of Ne gas under non-uniform axial magnetic field are reported. The self-excited ionization wave is damped and a different type of ionization wave is grown in the region of the strong magnetic field near the magnetic coils. The mode transitions appear on both sides of the magnetic coils where the magnetic field crosses a critical value.     

Ion cyclotron drift instability driven by cross-field current

An ion cyclotron drift instability is excited by a cross field current due to E_r × B drift of electrons and ion heating is observed in a plasma column in a magnetic field when a dc radial electric field E_r is applied.