The action of Vlasov waves on the velocity distribution in a plasma

1961 ◽  
Vol 10 (3) ◽  
pp. 473-479 ◽  
Author(s):  
J. W. Dungey
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Velocity Distribution ◽  
Thermal Equilibrium ◽  
Limited Range ◽  
Dimensional Model ◽  
One Dimensional ◽  
A Current

A one-dimensional model with no magnetic field is considered. It is supposed that the plasma starts in thermal equilibrium and then a current is forced to grow. Instability leads to the growth of waves, which are shown to stir the distribution in phase space, but only over a limited range of velocity. It is concluded that in order to restore stability the energy in the wave must become comparable to the energy of drift.

THE 2-D SEXTIC HAMILTONIAN OSCILLATOR

2013 ◽  
Vol 23 (06) ◽  
pp. 1330019
Author(s):  
F. J. MOLERO ◽  
J. C. VAN DER MEER ◽  
S. FERRER ◽  
F. J. CÉSPEDES
Keyword(s):  
Phase Space ◽  
Elliptic Functions ◽  
Singular Values ◽  
Nonlinear Oscillators ◽  
Momentum Mapping ◽  
Dimensional Model ◽  
Integrable Hamiltonian Systems ◽  
One Dimensional ◽  
Dimensional Phase Space ◽  
The One

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.

scholarly journals The structure of a hydromagnetic front in a cold collision-free plasma

1962 ◽  
Vol 12 (1) ◽  
pp. 81-87 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Magnetic Field ◽  
Characteristic Frequency ◽  
Cold Plasma ◽  
Equations Of Motion ◽  
One Dimensional ◽  
Infinite Extent ◽  
Cold Collision ◽  
The Magnetic Field ◽  
Free Plasma ◽  
A Current

A one-dimensional steady solution of the equations of motion of a cold plasma in a magnetic field is obtained. The plasma is of semi-infinite extent, bounded by a plane interface which separates it from a vacuum or medium at rest. The particles approach from infinity, are reflected at the front, and return to infinity in the opposite direction. At infinity, the magnetic field is parallel and anti-parallel to the plasma streams, and is inclined at an angle to the normal to the interface. The front is a current sheet across which the lines of force are bent, with the component of the magnetic field in the plane of the front changing direction. The inertia of the electrons is neglected, and the characteristic frequency associated with the front is the ion gyro-frequency.

scholarly journals The two-spin model of a tracking chamber: a phase-space perspective

2021 ◽  
Author(s):  
Luigi Barletti
Keyword(s):  
Phase Space ◽  
Spin Model ◽  
Space Representation ◽  
Dimensional Model ◽  
Wigner Matrix ◽  
One Dimensional ◽  
Classical Localization ◽  
Relationship Of ◽  
The Relationship ◽  
Phase Space Representation

AbstractWe study the dynamics of classical localization in a simple, one-dimensional model of a tracking chamber. The emitted particle is represented by a superposition of Gaussian wave packets moving in opposite directions, and the detectors are two spins in fixed, opposite positions with respect to the central emitter. At variance with other similar studies, we give here a phase-space representation of the dynamics in terms of the Wigner matrix of the system. This allows a better visualization of the phenomenon and helps in its interpretation. In particular, we discuss the relationship of the localization process with the properties of entanglement possessed by the system.

scholarly journals Analysis of Injected Electron Beam Propagation in a Planar Crossed-Field Gap

2021 ◽  
Vol 11 (6) ◽  
pp. 2540
Author(s):  
Ranajoy Bhattacharya ◽  
Adam M. Darr ◽  
Allen L. Garner ◽  
Jim Browning
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Critical Current Density ◽  
Critical Current ◽  
Current Density ◽  
Three Dimensional ◽  
One Dimensional ◽  
Field Device ◽  
The Magnetic Field ◽  
A Current

This paper examines basic crossed-field device physics in a planar configuration, specifically electron beam perturbation and instability as a function of variation in magnetic field, and angle between magnetic and electric field. We perform a three-dimensional (3-D) simulation of electron perturbation in a planar crossed-field system using the full 3-D particle trajectory solver in CST Particle Studio (CST-PS). The structure has a length, height, width and anode-sole gap of 15 cm, 2 cm, 10 cm, and 2 cm, respectively. The anode to sole voltage is fixed at 3 kV, and the magnetic field and injected current varied from 0.01 T to 0.05 T and 1.5 mA to 1 A, respectively. The simulations show that applying a magnetic field of 0.05 T makes the beam stable for a critical current density of 94 mA/cm2 for an anode-sole gap of 20 mm. Above this current density, the beam was unstable, as predicted. Introducing a 1° tilt in the magnetic field destabilizes the beam at a current density of 23 mA/cm2, which is lower than the critical current density for no tilt, as predicted by our theory. The simulation results also agree well with prior one-dimensional (1-D) theory and simulations that predict stable bands of current density for a 5° tilt where the beam is stable at low current density (<13.3 mA/cm2), unstable above this threshold, and then stable again at higher current density, (>33 mA/cm2).

scholarly journals Phase-space holes due to electron and ion beams accelerated by a current-driven potential ramp

2003 ◽  
Vol 10 (1/2) ◽  
pp. 37-44 ◽  
Author(s):  
M. V. Goldman ◽  
D. L. Newman ◽  
R. E. Ergun
Keyword(s):  
Phase Space ◽  
Electric Field ◽  
Double Layer ◽  
Ion Beams ◽  
Double Layers ◽  
Open Boundary ◽  
Neutral Density ◽  
One Dimensional ◽  
Slow Moving ◽  
A Current

Abstract. One-dimensional open-boundary simulations have been carried out in a current-carrying plasma seeded with a neutral density depression and with no initial electric field. These simulations show the development of a variety of nonlinear localized electric field structures: double layers (unipolar localized fields), fast electron phase-space holes (bipolar fields) moving in the direction of electrons accelerated by the double layer and trains of slow alternating electron and ion phase-space holes (wave-like fields) moving in the direction of ions accelerated by the double layer. The principal new result in this paper is to show by means of a linear stability analysis that the slow-moving trains of electron and ion holes are likely to be the result of saturation via trapping of a kinetic-Buneman instability driven by the interaction of accelerated ions with unaccelerated electrons.

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