H. Schamel

Hole equilibria in Vlasov–Poisson systems: A challenge to wave theories of ideal plasmas

A unified description of weak hole equilibria in collisionless plasmas is given. Two approaches, relying on the potential method rather than on the Bernstein, Greene, Kruskal method and associated with electron and ion holes, respectively, are shown to be equivalent. A traveling wave solution is thereby uniquely characterized by the nonlinear dispersion relation and the “classical” potential V(φ), which determine the phase velocity and the spectral decomposition of the wave structure, respectively. A new energy expression for a hole carrying plasma is found. It is dominated by a trapped particle contribution occurring one order earlier in the expansion scheme than the leading term in conventional schemes based on a truncation of Vlasov’s equation. Linear wave theory— reconsidered by taking the infinitesimal amplitude limit—is found to be deficient, as well. Neither Landau nor van Kampen modes and their general superpositions can adequately describe these trapped particle modes due to an incorrect treatmen...

The true nature of space-charge-limited currents in electron vacuum diodes: A Lagrangian revision with corrections

The physics of space-charge-limited current (JSCL) in diodes with finite electron injection velocities v0 is investigated within the Lagrangian flow description. The space-charge-limited (SCL) current is shown to be given by JSCL=(X+1+X2)3JCL, where JCL∼U3/2/L2 is the familiar Child–Langmuir current, X=(mv02/2eU)1/2, U and L are the diode voltage and length, respectively. It results from an intrinsic property of the diode rather than from electron reflexion, the current picture of SCL accepted since Langmuir’s days. For field emitted electrons, on the other hand, JCL is proved to be universally valid, because in this case v0=0 holds. A number of further diode properties are derived analytically and presented numerically.

Quantum corrected electron holes

Abstract The theory of electron holes is extended into the quantum regime. The Wigner–Poisson system is solved perturbatively based in lowest order on a weak, standing electron hole. Quantum corrections are shown to lower the potential amplitude and to increase the number of deeply trapped electrons. They, hence, tend to bring this extreme non-equilibrium state closer to thermodynamic equilibrium, an effect which can be attributed to the tunneling of particles in this mixed state system.

Kinetic theory of periodic hole and double layer equilibria in pair plasmas

The existence of manifestly nonlinear electrostatic modes in pair plasmas is shown analytically by means of the quasi-potential method applied to the Vlasov?Poisson system. These modes owe their existence to the trapping of particles in the potential trough(s) and are typically characterized by a notch in the particle distribution functions at resonant velocity, forming vortices in phase space. Both entities, wave structure ?(x) and phase velocity v0, are uniquely characterized by two parameters, the periodicity parameter k0 and the spectral parameter B. Whereas k0 = 0 describes double layers, with a phase velocity in the thermal range, k0 ? 0 represents a periodic wave train which can propagate with two rather distinct phase velocities. One is related to the fast plasma wave, the other one to the slow acoustic mode.

Cnoidal electron hole propagation: Trapping, the forgotten nonlinearity in plasma and fluid dynamics

In this review a plaidoyer is held for a specific form of nonlinearity, the trapping nonlinearity (TN), which arises due to a capture of particles and/or fluid elements in an excited coherent structure. This is of some importance since it appears that TN has not yet taken roots hitherto, neither in turbulence nor in anomalous transport models. The present state of knowledge about wave excitation, seen numerically and experimentally, especially at space craft, however, speaks a different language suggesting that current wave models are constructed too narrowly to reflect reality. The focus is on traveling cnoidal electron holes (CEHs) in electrostatically driven plasmas and the physical world associated with these. As a result a new wave concept emerges, in which the low amplitude dynamics is nonlinearly controlled by TN.

Collective diode dynamics: an analytical approach

Abstract An analytical study of the plasma states in nonneutral plasma diodes and of their stability is presented for an arbitrary neutralization parameter γ , including the Pierce ( γ =1) and the Bursian ( γ =0) diode as special cases. Physically such a study is of interest, e.g. in the transport problem of an electron beam in spatially bounded electronic devices. Similarity transformations are obtained which connect equilibrium solutions of different γ s. This implies that by simple transformations one can infer from equilibria of the generalized Pierce diode to equilibria of nonneutral diodes. The regimes with partial and total reflection of electrons are studied in detail for the first time. A classification of nonuniform solutions for these regions as well as for the regime without reflection is presented. The equivalence between the Eulerian and the Lagrangian formulation of the diode dynamics is proved, and both, the aperiodical and oscillatory eigenmodes of the generalized Pierce diode are examined. New bifurcation points in the branches of dispersion relations are discovered.

Observation and characterization of laser-driven Phase Space Electron Holes

The direct observation and full characterization of a phase space electron hole (EH) generated during laser-matter interaction is presented. This structure, propagating in a tenuous, nonmagnetized plasma, has been detected via proton radiography during the irradiation with a ns laser pulse (Iλ2≈1014 W/cm2) of a gold hohlraum. This technique has allowed the simultaneous detection of propagation velocity, potential, and electron density spatial profile across the EH with fine spatial and temporal resolution allowing a detailed comparison with theoretical and numerical models.

On the physics of the plasma maser

Abstract We consider the plasma-maser interactions of electrostatic waves for both magnetized and unmagnetized plasmas. The difference between these two cases is clarified. A correct transition to the zero magnetic field is presented. The accuracy of the conservation of the adiabatic invariant (the number of quanta of the nonresonant waves) is calculated.

Nonlinear instability and saturation of linearly stable current-carrying pair plasmas

The nonlinear instability of current-carrying pair plasmas is investigated with a Vlasov–Poisson model for the two-particle species. It is shown that linearly stable configurations are unstable against small incoherent perturbations of the particle distribution functions. The instability gives rise to a self-acceleration and growth of phase-space holes. After the growth of the phase-space holes, the instability reaches a chaotic saturation where the finite-amplitude holes interact and merge, and after a long time, the system attains a stable equilibrium state with a smaller drift and a larger temperature than the initial one, and where a few stable phase-space holes are present.

Arbitrary potential drops between collector and emitter in pure electron diodes

A novel Lagrangian integral formalism is applied to pure electron diodes. Analytical expressions are obtained in terms of the injected current and of the potential drop for two DC states. These two states are either completely transmitted flows or flows with partial reflection at a virtual cathode. Splitting rates and other quantities are presented for arbitrary potentials.