Plasma-vacuum Interface Research Articles

Characterization of laser-generated aluminum plasma using ion time-of-flight and optical emission spectroscopy

Laser plasma generated by ablation of an Al target in vacuum is characterized by ion time-of-flight combined with optical emission spectroscopy. A Q-switched Nd:YAG laser (wavelength λ = 1064 nm, pulse width τ ∼ 7 ns, and fluence F ≤ 38 J/cm2) is used to ablate the Al target. Ion yield and energy distribution of each charge state are measured. Ions are accelerated according to their charge state by the double-layer potential developed at the plasma-vacuum interface. The ion energy distribution follows a shifted Coulomb-Boltzmann distribution. Optical emission spectroscopy of the Al plasma gives significantly lower plasma temperature than the ion temperature obtained from the ion time-of-flight, due to the difference in the temporal and spatial regions of the plasma plume probed by the two methods. Applying an external electric field in the plasma expansion region in a direction parallel to the plume expansion increases the line emission intensity. However, the plasma temperature and density, as measured by optical emission spectroscopy, remain unchanged.

Surface currents associated with external kink modes in tokamak plasmas during a major disruption

The surface current on the plasma-vacuum interface during a disruption event involving kink instability can play an important role in driving current into the vacuum vessel. However, there have been disagreements over the nature or even the sign of the surface current in recent theoretical calculations based on idealized step-function background plasma profiles. We revisit such calculations by replacing step-function profiles with more realistic profiles characterized by strong but finite gradient along the radial direction. It is shown that the resulting surface current is no longer a delta-function current density, but a finite and smooth current density profile with internal structure, concentrated within the region with strong plasma pressure gradient. Moreover, this current density profile has peaks of both signs, unlike the delta-function case with a sign opposite to, or the same as the plasma current. We show analytically and numerically that such current density can be separated into two parts, with one of them, called the convective current density, describing the transport of the background plasma density by the displacement, and the other part that remains, called the residual current density. It is argued that consideration of both types of current density is important and can resolve past controversies.

Numerical study of the wave-break in the vacuum-plasma interface during the interaction of an intense laser pulse

In this paper, the wave break in the plasma-vacuum interface during the intense laser interaction is investigated. Since the nonlinear wave breaking is a non-adiabatic process, the fully kinetic 1D-3V Particle-In-Cell (PIC) simulation experiments are performed to identify whether that the origin of this mechanism is electromagnetic or electrostatic. Our simulation results show that the nonlinear wave breaking on the vacuum-plasma interface has electrostatic origin. In addition, it is found that for pulse lengths exceeding the plasma wavelength this electrostatic phenomenon comes in conjunction with some active electromagnetic effects having the same impact on the electron acceleration. In these regards, we conduct sophisticated simulations isolating these electromagnetic effects and study the effects of the pulse parameters such as the pulse rise time, pulse length, and pulse shape on the boundary nonlinear wave breaking. The study of the pulse rise-time variation effects shows that as the rise time of the laser pulse decreases, the number of the electrons involved in the nonlinear wave breaking, maximum energy of the trapped electrons and the path length of the accelerated electrons in the phase space are increased. Also, the study of phase space and field patterns in our simulation indicates that the reduction of the pulse flat top duration time causes that the smaller part of the electrons and the smaller portion of the wake wave involve in the nonlinear wave breaking.

On the Motion of Free Interface in Ideal Incompressible MHD

For the free boundary problem of the plasma-vacuum interface to three-dimensional ideal incompressible magnetohydrodynamics (MHD), the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of view and some quantities such as the second fundamental form and the velocity of the free interface are estimated. In the vacuum region, the magnetic fields are described by the div-curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic fields are tangent to the interface, but we do not need any restrictions on the size of the magnetic fields on the free interface. We introduce the "virtual particle" endowed with a virtual velocity field in vacuum to reformulate the problem to a fixed boundary problem under the Lagrangian coordinates. The $L^2$-norms of any order covariant derivatives of the magnetic fields both in vacuum and on the boundaries are bounded in terms of initial data and the second fundamental forms of the free interface and the rigid wall. The estimates of the curl of the electric fields in vacuum are also obtained, which are also indispensable in elliptic estimates.

Weak stability of the plasma–vacuum interface problem

We consider the free boundary problem for the two-dimensional plasma–vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary.We study the linear stability of rectilinear plasma–vacuum interfaces by computing the Kreiss–Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma–vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity.We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss–Lopatinskiĭ condition, as the Kreiss–Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss–Lopatinskiĭ condition may fail simultaneously.

Catastrophic instabilities of modified DA-DC hybrid surface waves in a semi-bounded plasma system

We find the catastrophic instabilities and derive the growth rates for the dust-cyclotron resonance (DCR) and dust-rotation resonance (DRR) modes of the modified dust-acoustic and dust-cyclotron (DA-DC) hybrid surface waves propagating at the plasma–vacuum interface where the plasma is semi-bounded and composed of electrons and rotating dust grains. The effects of magnetic field and dust rotation frequency on the DCR- and DDR-modes are also investigated. We find that the dust rotation frequency enhances the growth rate of DCR-mode and the effect of dust rotation on this resonance mode decreases with an increase of the wave number. We also find that an increase of magnetic field strength enhances the DCR growth rate, especially, for the short wavelength regime. In the case of DRR-mode, the growth rate is found to be decreased less sensitively with an increase of the wave number compared with the case of DCR, but much significantly enhanced by an increase of dust rotation frequency. The DRR growth rate also decreases with an increase of the magnetic field strength, especially in the long wavelength regime. Interestingly, we find that catastrophic instabilities occur for both DCR- and DRR-modes of the modified DA-DC hybrid surface waves when the rotational frequency is close to the dust-cyclotron frequency. Both modes can also be excited catastrophically due to the cooperative interaction between the DCR-mode and the DRR-mode.

Picosecond laser-driven terahertz radiation from large scale preplasmas of solid targets

The terahertz (THz) radiation from the front of solid targets with a large-scale preplasma irradiated by relativistic picosecond laser pulses has been studied. The THz radiation measured at the specular direction nonlinearly increases with laser energy and an optimal plasma density scalelength is observed. Particle-in-cell simulations indicate that the radiation can be attributed to the model of mode conversion. While the THz radiation near the target normal direction is saturated with laser energy and plasma scalelength. Unlike the radiation in the specular direction’ the transient current formed at the plasma-vacuum interface could be responsible for the radiation near the target normal.

Data dependence for the amplitude equation of surface waves

We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891–897, 1995), surface waves on current-vortex sheets in incompressible MHD (Ali and Hunter in Q Appl Math 61(3):451–474, 2003; Ali et al. in Stud Appl Math 108(3):305–321, 2002) and on the incompressible plasma–vacuum interface (Secchi in Q Appl Math 73(4):711–737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247–267, 2006), Secchi (Q Appl Math 73(4):711–737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.

Saturated ideal kink/peeling formations described as three-dimensional magnetohydrodynamic tokamak equilibrium states

Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasma-vacuum interface are computed for the first time. The structures obtained have the appearance of saturated ideal external kink/peeling modes. High edge pressure gradients yield toroidal mode number n = 1 corrugations for a high edge bootstrap current and larger n distortions when this current is small. Deformations in the plasma boundary region induce a nonaxisymmetric Pfirsch-Schlüter current driving a field-aligned current ribbon consistent with reported experimental observations. A variation in the 3D equilibrium confirms that the n = 1 mode is a kink/peeling structure. We surmise that our calculated equilibrium structures constitute a viable model for the edge harmonic oscillations and outer modes associated with a quiescent H-mode operation in shaped tokamak plasmas.

Terahertz emission from two-plasmon-decay induced transient currents in laser-solid interactions

We have studied the generation of terahertz (THz) radiation via the interaction of intense femtosecond laser pulses with solid targets at a small incidence angle. It is found that preplasma with a moderate density gradient can enhance the emission. We also observe saturation of the THz output with the driving laser energy. We find that THz emission is closely related to the 3/2 harmonics of the driving laser. Particle-in-cell simulations indicate that under the present experimental conditions, the THz emission could be attributed to the transient currents at the plasma-vacuum interface, mainly formed by the two-plasmon-decay instability.

A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma–vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number $n=1$ distortions when the edge bootstrap current is large and higher $n$ corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch–Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch–Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.

Nonlinear surface waves on the plasma-vacuum interface

In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagates along the plasma-vacuum interface when it is linearly weakly stable. Following the approach of Ali and Hunter (2003), we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive a blow up criterion.

Simple scalings for various regimes of electron acceleration in surface plasma waves

Different electron acceleration regimes in the evanescent field of a surface plasma wave are studied by considering the interaction of a test electron with the high-frequency electromagnetic field of a surface wave. The non-relativistic and relativistic limits are investigated. Simple scalings are found demonstrating the possibility to achieve an efficient conversion of the surface wave field energy into electron kinetic energy. This mechanism of electron acceleration can provide a high-frequency pulsed source of relativistic electrons with a well defined energy. In the relativistic limit, the most energetic electrons are obtained in the so-called electromagnetic regime for surface waves. In this regime, the particles are accelerated to velocities larger than the wave phase velocity, mainly in the direction parallel to the plasma-vacuum interface.

On well-posedness of the plasma-vacuum interface problem: the case of non-elliptic interface symbol

We consider the plasma-vacuum interface problem in a classical statement when in the plasma region the flow is governed by the equations of ideal compressible magnetohydrodynamics, while in the vacuum region the magnetic field obeys the div-curl system of pre-Maxwell dynamics. The local-in-time existence and uniqueness of the solution to this problem in suitable anisotropic Sobolev spaces was proved in [17], provided that at each point of the initial interface the plasma density is strictly positive and the magnetic fields on either side of the interface are not collinear. The non-collinearity condition appears as the requirement that the symbol associated to the interface is elliptic. We now consider the case when this symbol is not elliptic and study the linearized problem, provided that the unperturbed plasma and vacuum non-zero magnetic fields are collinear on the interface. We prove a basic a priori $L^2$ estimate for this problem under the (generalized) Rayleigh-Taylor sign condition $[\partial q/\partial N]<0$ on the jump of the normal derivative of the unperturbed total pressure satisfied at each point of the interface. By constructing an Hadamard-type ill-posedness example for the frozen coefficients linearized problem we show that the simultaneous failure of the non-collinearity condition and the Rayleigh-Taylor sign condition leads to Rayleigh-Taylor instability.

On the normal-mode frequency spectrum of kinetic magnetohydrodynamics

This paper presents an explicit proof that, in the kinetic magnetohydrodynamics framework, the squared frequencies of normal-mode perturbations about a static equilibrium are real. This proof is based on a quadratic form for the square-integrable normal-mode eigenfunctions and does not rely on demonstrating operator self-adjointness. The analysis is consistent with the quasineutrality condition without involving any subsidiary constraint to enforce it, and does not require the assumption that all particle orbits be periodic. It applies to Maxwellian equilibria, spatially bounded by either a rigid conducting wall or by a plasma-vacuum interface where the density goes continuously to zero.

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated. The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate. The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers. The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations. The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma–vacuum interface. The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.

Stability of the linearized MHD-Maxwell free interface problem

We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields, in order to investigate the well-posedness of the problem, in particular in relation with the electric field in vacuum. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary.Under suitable stability conditions satisfied at each point of the plasma-vacuum interface, we derive a basic a priori estimate for solutions to the linearized problem in the Sobolev space $H^1_{\tan}$ with conormal regularity. The proof follows by a suitable secondary symmetrization of the Maxwell equations in vacuum and the energy method.An interesting novelty is represented by the fact that the interface is characteristic with variable multiplicity, so that the problem requires a different number of boundary conditions, depending on the direction of the front velocity (plasma expansion into vacuum or viceversa). To overcome this difficulty, we recast the vacuum equations in terms of a new variable which makes the interface characteristic of constant multiplicity. In particular, we don't assume that plasma expands into vacuum.

Kinetic Theory of Electrostatic Surface Waves in a Magnetized Plasma Slab

The dispersion relation of electrostatic surface waves propagating in a magnetized plasma slab is derived from Vlasov-Poisson equations under the specular reflection boundary condition. We consider the case that the static magnetic field is parallel to the plasma-vacuum interface and the surface wave propagates obliquely to the magnetic field on the parallel plane. We find that the specular reflection boundary conditions on the plasma slab-vacuum boundaries can be satisfied, even in a magnetized plasma, by simple extension of the electric potential into the vacuum region, due to the inherent symmetry of the distribution function. Utilizing an invariance property of the kinetic surface wave solution, it is shown that the two-mode structure of the surface wave yields the symmetric and anti-symmetric modes. The kinetic dispersion relation is checked against the dispersion relations obtained from fluid equations and shows complete agreement.

Well-posedness of the linearized plasma-vacuum interface problem in ideal incompressible MHD

We study the free boundary problem for the plasma-vacuum interface in ideal incompressible magnetohydrodynamics (MHD). In the vacuum region the magnetic field is described by the div-curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic field is tangent to the boundary. Under a suitable stability condition satisfied at each point of the plasma-vacuum interface, we prove the well-posedness of the linearized problem in Sobolev spaces.

Influence of vacuum electric field on the stability of a plasma-vacuum interface

We study the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics. Unlike the classical statement, when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. We show that a sufficiently large vacuum electric field can make the planar interface violently unstable. We find and analyze a sufficient condition on the vacuum electric field that precludes violent instabilities. Under this condition satisfied at each point of the unperturbed nonplanar plasma-vacuum interface, we prove the well-posedness of the linearized problem in anisotropic weighted Sobolev spaces.