Simulation of the dynamics of resistive hose instability of a relativistic electron beam propagating in a resistive plasma channel with arbitrary conductivity

The spatial dynamics of the resistive hose instability of a relativistic electron beam has been studied for the case when the charge neutralization time is much longer, on the order of, or much shorter than the current compensation time. It has been found that the growth of this instability has the highest increment when the charge neutralization time is on the order of skin time.

     

On a class of exact geodesics of the erez-rosen metric

In a previous paper, a class of exact geodesics for the motion of a particle in a gravitational-monopole-prolate-quadrupole field was investigated, both in Newtonian mechanics and in general relativity. This paper consists of both an amplification of the analysis contained in the previous paper and an extension of the analysis to the case for negative quadrupole moment, which was not treated previously. The relativistic results are based on the monopole-quadrupole metric of Erez and Rosen, the Newtonian results on the monopole-quadrupole potential of Laplace. In the limit of vanishing quadrupole parameter (q 0), the relativistic results reduce to those of the familiar Schwarzschild case; in the weak-field limit (r/m ), the relativistic results reduce to those of the Newtonian case. The existence and stability thresholds in the relativistic case yield values that uniquely characterize the Erez-Rosen metric.     

On Transient Time Reduction of a 2.4 GHz Relativistic Traveling Wave Oscillator with a Hollow Slow Wave System

The decrease in the transient time in a relativistic microwave traveling wave oscillator, in which the interaction is carried out between the relativistic electron beam and the fundamental harmonic of the forward-traveling electromagnetic wave slowed down to the speed of light in the hollow slow wave system system, has been numerically and experimentally demonstrated. It is shown that in this mode a high beam-to-wave coupling impedance up to ≈10 Ω is achieved, which ensures reduction of the transient time. In the experiment, a microwave peak power of 210 ± 30 MW at a frequency of 2.45 GHz in a guiding magnetic field of 0.16 T was obtained. The efficiency of the oscillator to convert the power of the electron beam into microwave power was 17 ± 3%. At the beam current pulse duration of about 50 ns the microwave pulse duration was about 20 ns and the transient time was about 22 ns.

     

Beam of Ultrarelativistic Particles and Cherenkov Resonance

Earlier, we reported on registration of three sequential events with energies greater than 10¹⁹ eV with two installations of EAS (Yakutsk and Telescope Arrays) for one day. Here we take into account that a moving relativistic source creates a particle beam due to the Cherenkov effect. In this case, with a certain orientation of the direction of movement of the source relative to the observer and direction of the interstellar magnetic field, there is a mechanism that allows to explain the observed sequence of the recorded events.

     

Equation of State of Tantalum and Plutonium in a Spherical Cell Approximation and at Extremely High Pressures

We first present the equation of state (EOS) of a relativistic homogeneous electron gas in the exchange only approximation. We then go on to use this result to determine approximately the EOS of the heavy metals Pu and Ta. An essential ingredient is the electron density at the boundary of the Wigner-Seitz polyhedron and we determine this density using relativistic Thomas-Fermi theory.     

Form factor of a relativistic two-particle system within the relativistic quasipotential approach: Case of an arbitrary masses and a scalar current

A new relativistic form factor for a bound two-particle system was obtained for the case of a scalar current. The respective analysis was performed within the relativistic quasipotential approach based on a covariant Hamiltonian formulation of quantum field theory by going over to a three-dimensional relativistic configuration representation for the case of the interaction of two relativistic spinless particles that have arbitrary masses.     

Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength

We compute, via a variational mixed-base method, the energy spectrum of a two-dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find that the relativistic spectrum does not present s states.     

Effect of Multiple Scattering of a Relativistic Electron Beam in a Gas–Plasma Medium on the Dynamics of the Resistive Hose Instability

We consider the effect of the multiple Coulomb scattering on the spatial dynamics of the relativistic hose instability of a relativistic electron beam propagating along an Ohmic plasma channel. It is shown that the enhancement of scattering noticeably suppresses this instability.

     

Hamiltonian for a Relativistic Particle with Linear Dissipation

A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The hamiltonian for a relativistic particle with linear dissipation is obtained. An example of this approach is given. PACS: 45.20.Jj     

Momentum Space Diffusion from Spatially Amplified Waves in a Plasma in a Magnetic Field

Quasilinear equations for relativistic plasmas in external magnetic fields are derived for the case of spatially growing wave turbulence. This generalizes the well-known quasilinear approach to an amplifying relativistic plasma. The equations can be cast in condensed momentum-space diffusive form. The diffusion tensor is given. As a result an inhomogeneity is produced in the space charge distribution giving rise to the development of a second-order field-aligned dc electric field. A general formula for the electrostatic potential is presented, which is specialised to the case of ion-cyclotron turbulence. Here the field points out of the interaction region.     

Decoherence and Phase Transitions in Quantum Dynamics

A particle with internal degrees of freedom is in contact with a bath of photons (necessitating a relativistic treatment). The occurrence of decoherence is established and the density matrix is found to be diagonal in momentum space. In the case of non-trivial internal degrees of freedom and selection rules there is a first order phase transition separating those degrees of freedom. Finally, because probability amplitudes become probabilities, Einstein’s proposal that more than one detector could respond to a signal is answered.

     

Relativistic quantum particle in a homogeneous external field

The model of the relativistic quantum particle in a homogeneous external field is proposed. This model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space in our case is the one-dimensional Lobachevsky space. We have found the wave functions and propagator for the model under study in both x- and p-representations.     

Structure formation in the presence of relativistic heat conduction: corrections to the Jeans wave number with a stable, first order in the gradients, formalism

The problem of structure formation in relativistic dissipative fluids was analyzed in a previous work within Eckart’s framework, in which the heat flux is coupled to the hydrodynamic acceleration, additional to the usual temperature gradient term. It was shown that in such case, the pathological behavior of fluctuations leads to the disappearance of the gravitational instability responsible for structure formation (Mondragon-Suarez and Sandoval-Villalbazo in Gen Relativ Gravit 44:139–145, 2012). In the present work the problem is revisited using a constitutive equation derived from relativistic kinetic theory. This new relation, in which the heat flux is not coupled to the hydrodynamic acceleration, leads to a consistent first order in the gradients formalism. In this case the gravitational instability remains, and only relativistic corrections to the Jeans wave number are obtained. In the calculation here shown the non-relativistic limit is recovered, opposite to what happens in Eckart’s case (Hiscock and Lindblom in Phys Rev D 31:725–733, 1985).     

Statistical mechanics of relativistic plasmas

Based on the Klimontovich method of construction of a relativistic statistical mechanics the binary correlation function of a relativistic plasma is considered. Up to the order e⁴ for spatially homogeneous systems the relativistic binary correlation function can be expressed by the relativistic dielectric tensor, where higher-order correlation functions are neglected.In the case of thermodynamic equilibrium the relativistic dielectric tensor is calculated. The corresponding binary correlation function is determined up to the first relativistic order. The result is compared with those of Trubnikov/Kosachev (1968) and Krizan (1969).     

Effect of Temporal Current Modulation on the Tracking Force Acting on a Relativistic Electron Beam in an Ohmic Plasma Channel

The effect of the current rise time in a relativistic electron beam pulse on the tracking force exerted by the low-conductivity Ohmic plasma channel on the beam has been analyzed using the “hard” beam model. It is shown using numerical analysis that an increase in the beam current rise time substantially reduces the tracking force considered here.

     

On Relativistic Mass Spectra of a Two-Particle System

Abstract

A relativistic two-particle system with time-asymmetric scalar and vector interactions in the two-dimensional space-time is considered within the frame of the front form of dynamics using the dynamical symmetry approach. The mass-shell equation may be represented in terms of the nonlinear canonical realization of the Lie algebra of the group SO(2, 1). This allows us to quantize the system and to obtain a closed form for the mass spectrum.     

Drift theory of charged-particle motion for a strong electric field in a weakly relativistic approximation

Drift equations of motion are derived for a charged particle in the case of a strong electric field with allowance for relativistic effects of order v²/c². The role of these effects is discussed along with the effects of a high-frequency field. The cases of weak and strong electric fields are distinguished [2] in the drift theory of the motion of charged particles in weakly inhomogeneous magnetic and electric fields. In the case of a weak electric field, the electric-drift velocity is v_E v, where v is the characteristic velocity of the particle. For a strong electric field,v _Ev.The drift theory has now been reasonably well developed for the case of weak electric fields in the classical and relativistic cases, for the absence of high-frequency fields and for the presence of these [1–3], Extension of the theory to strong electric fields involves considerable mathematical difficulties, and this has been done only in the classical approximation with and without hf fields [2–4], Here we consider the drift theory of charged-particle motion for the case of a strong electric field in the weakly relativistic approximation, incorporating terms of order v²/c², where c is the velocity of light. Also hf fields may be present.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–9, September, 1981.     

The emission positions of kHz QPOs and Kerr spacetime influence

Based the Alfven wave oscillation model (AWOM) and relativistic precession model (RPM) for twin kHz QPOs, we estimate the emission positions of most detected kHz QPOs to be at r=18+/−3 km (R/15 km), except Cir X-1 at r∼30+/−5 km (R/15 km). For the proposed Keplerian frequency as an upper limit to kHz QPO, the spin effects in Kerr Spacetime are discussed, which have about a 5% (2%) modification for that of the Schwarzchild case for the spin frequency of 1000 (400) Hz. The application to the four typical QPO sources, Cir X-1, Sco X-1, SAX J1808.4-3658 and XTE 1807-294, is mentioned.

     

On The Contribution of the P and D Partial-Wave States to the Binding Energy of the Triton in the Bethe-Salpeter-Faddeev Approach

The influence of the partial-wave states with nonzero orbital moment of the nucleon pair on the binding energy of the triton T(nnp) in the relativistic case is considered. The relativistic generalization of the Faddeev equation in the Bethe-Salpeter formalism is applied. Two-nucleon t matrix is obtained from the Bethe-Salpeter equation with separable kernel of nucleon-nucleon interaction of the rank one. The kernel form factors are the relativistic type of the Yamaguchi functions. The following two-nucleon partial-wave states are considered: ¹S₀, ³S₁, ³D₁, ³P₀, ¹P₁, ³P₁. The system of the integral equations are solved by using the iteration method. The binding energy of the triton and three-nucleon amplitudes are found. The contribution of the P and D states to the binding energy of triton is given.

     

Relativistic ponderomotive forces

The interaction of a relativistic classical electron with an inhomogeneous electromagnetic field is investigated. In second-order perturbation theory the motion is separated into fast and slow motions, and the relativistic Newtonian equation is averaged over the fast oscillations. The rate of change obtained for the slow component of the electron momentum is interpreted as a relativistic ponderomotive force. The result is generalized to the relativistic case of the wellknown expression for the Gaponov-Miller force acting on an electron at rest. The expressions obtained for the relativistic ponderomotive forces are very complicated in the general case. They simplify in the limit of a stationary field (pulses of long duration) and a small gradient. The most typical and simplest special case of an inhomogeneous field—a stationary plane-focused beam—is investigated. The main difference between relativistic ponderomotive forces and their nonrelativistic limit is they have multiple components. In addition to the usual force directed along the gradient of the field, the relativistic case is also characterized by force components that do not have the form of the gradient of a potential and are parallel to the wave vector and the direction of the field polarization. It is shown that when a relativistic electron travels in a direction close to the direction of the wave vector of a focused laser beam, these components can greatly exceed the gradient force. A force directed along the field polarization vector arises even when the gradient of the field in this direction is zero. Zh. éksp. Teor. Fiz. 116, 1198–1209 (October 1999)