Surface Ion-Sound Wave in Magnetic Arch With High Pressure Plasma

The work analytically substantiates the parameters of the surface wave found in numerical modelling of the collision of two oncoming supersonic plasma flows inside a magnetic arc in application to the experiment on the laboratory setup Solar Wind'' (Inst. Appl. Phys RAS). An ion-acoustic surface wave exists in the regime of dense plasma flows when their dynamic pressure is of the order of the pressure of an undisturbed magnetic field, so that the flows push the initial magnetic field out of their volume. The wave frequency is in the range between the ion gyrofrequencies inside the plasma bundle and in the outer region of the confining magnetic field. In the external rarefied medium, the near-surface structure is a heterogeneous magnetic sound, consistent in pressure and low total polarisation of the medium with the isotropic’’ ion sound confined from the inside in a dense plasma bundle. The energy of the structure is mainly contained in the kinetic energy of the wave motion of ions inside the tube. At the same time, the electric field strength is sharply increased outside. Firstly, the latter circumstance arises from the need to maintain a uniform electron electric drift velocity inside the transition layer. Secondly, the energetically weak ion sound propagating into the outer environment is close to electrostatic ion oscillations below the ion gyrofrequency in the external region, which are characterised by increased electric field strength across the ambient magnetic field.

💡 Research Summary

The paper investigates a surface ion‑acoustic wave that appears when two counter‑propagating supersonic plasma jets collide inside a magnetic arch, as realized in the laboratory “Solar Wind” experiment. The authors first describe the experimental configuration: a cylindrical vacuum chamber (diameter 183 mm, width 130 mm) equipped with two orthogonal solenoids that generate a quarter‑circle magnetic arch of radius 9 cm. The magnetic field is strongest at the solenoid cores (≈ 3.3 T) and drops to ≈ 0.12 T at the arch apex. An arc discharge on an aluminum cathode (10 mm diameter) produces plasma jets with ion densities ranging from 10¹³ to 10¹⁵ cm⁻³, ion charge state Z≈1.7, and flow speeds v_i≈15 km s⁻¹, which corresponds to a Mach number M≈3.5 relative to the ion‑sound speed c_s≈4.3 km s⁻¹.

Hybrid kinetic‑fluid simulations (the AKA scheme) are employed to model the system. Ions are treated kinetically, while electrons are modeled as a massless fluid whose momentum equation balances the electron pressure gradient against the total Lorentz force. Electron pressure evolves according to an anisotropic (CGL‑type) adiabatic law, and the electromagnetic fields are solved in the Darwin approximation, neglecting displacement currents appropriate for low‑frequency (ω ≪ ω_{Be}) dynamics.

A key finding is that when the dynamic pressure of each jet (p_pl = 2 n m v²) becomes comparable to the magnetic pressure of the background field (p_mag = B²/8π), the plasma expels the magnetic field from its interior, creating a low‑field “vacuum” region surrounding a high‑density plasma tube. In this regime the internal thermal pressure far exceeds the local magnetic pressure, while the expelled magnetic field confines the tube laterally. The collision at the arch apex then excites internal magnetohydrodynamic waves, among which a surface ion‑acoustic mode is identified.

The surface wave possesses several distinctive properties. Its wave vector has no component along the translational symmetry direction of the arch (k_τ = 0), meaning the disturbance is strictly normal to the interface. The frequency lies between the ion gyro‑frequencies of the dense interior plasma and the surrounding magnetic field, i.e. ω_{Bi} < ω ≪ min(ω_{Be}, ω_{pi}). Because ω ≪ ω_{Be} the electrons remain magnetized, whereas the ions are effectively unmagnetized, leading to a predominantly electrostatic character. The wave thickness is of order the inverse plasma wavenumber (≈ 1/κ_pl) and is much smaller than the wavelength, a consequence of the very large dielectric permittivity ε ≈ |ω_{pi}²/4π ω²| ≫ 1 in the low‑frequency regime.

Energy analysis shows that the majority of the wave’s energy is stored as kinetic energy of the ions moving within the tube, while the electric field amplitude is strongly amplified in the external rarefied medium. This amplification is required to maintain a uniform electron drift velocity across the transition layer; the drift ensures that the electrons remain frozen‑in to the magnetic field despite the strong density gradient. Consequently, the tangential electric field experiences a discontinuity in the laboratory frame, which disappears in the frame moving with the electron drift.

Four boundary conditions are imposed at the plasma‑magnetic interface: (1) balance of total (plasma + magnetic) pressure, (2) continuity of electron drift velocity on both sides, (3) continuity of the normal component of the electric displacement (polarization) D_n, and (4) continuity of the longitudinal component of the electric field along the magnetic field lines. Earlier magnetohydrodynamic treatments omitted conditions (2) and (3), thereby missing the outward‑propagating electrostatic ion‑acoustic component and its associated attenuation mechanism.

The authors compare the laboratory situation with the Earth’s magnetopause, where the solar wind forms a magnetosheath that flows around the magnetosphere. In both cases a high‑pressure plasma pushes against a lower‑pressure magnetic field, creating a sharp boundary. However, the classic Kelvin‑Helmholtz instability, often invoked for magnetopause surface waves, does not operate here because the external Alfvén speed (c_A ≫ v_i) suppresses the instability. Instead, the surface ion‑acoustic wave is driven by the pressure imbalance and the requirement of a uniform electron drift, making it the dominant surface mode under the experimental conditions.

Quantitatively, at the arch apex the magnetic field is B_top ≈ 0.1 T, giving p_mag ≈ 4 × 10⁴ dyn cm⁻². For a typical jet density n_i ≈ 10¹⁵ cm⁻³ and speed v_i ≈ 15 km s⁻¹, the dynamic pressure is p_pl ≈ 2.3 × 10⁴ dyn cm⁻², i.e. of the same order as p_mag. Simulations under these parameters reveal a surface wave confined to a layer of roughly one millimetre thickness, with the electric field outside the tube amplified by an order of magnitude relative to the interior.

In summary, the paper provides a comprehensive analytical and numerical validation of a surface ion‑acoustic wave that arises when high‑pressure plasma flows expel the confining magnetic field in a magnetic arch. The work elucidates the necessary pressure balance, the role of electron drift continuity, and the specific frequency window that permits the wave to exist. By linking the laboratory findings to space‑plasma analogues, the study suggests that similar surface ion‑acoustic modes may be relevant in astrophysical contexts where plasma pressure rivals magnetic pressure, such as at planetary magnetopauses or in solar coronal loops undergoing rapid energy release.