Energetic-particle-driven modes in magnetically confined fusion plasmas often exhibit nonlinear frequency sweeping ('chirping'), reflecting complex wave-particle interactions near marginal stability. While the bump-on-tail (BOT) instability within the Berk-Breizman framework has served as a canonical model for understanding such phenomena, a unified nonlinear description remains incomplete when drag, diffusion, and Krook relaxation act simultaneously. In this work, we present a comprehensive numerical investigation of the BOT instability that explicitly retains all three collision operators together with external wave damping. Using a validated characteristic-based BOT code, we systematically scan the multi-dimensional collision parameter space and construct nonlinear regime maps and bifurcation diagrams. To organize the rich dynamics, we introduce a two-level categorization that combines global wave-energy evolution (damped, steady, periodic, and chaotic states) with chirping subtypes identified from spectral morphology. We find that diffusion and Krook relaxation regularize the nonlinear dynamics and promote ordered transitions from chaotic behaviors to periodic oscillations and steady saturation as collision strength increases, with the saturation level decreasing approximately exponentially with external damping. In contrast, drag alone does not admit steady solutions and instead drives persistent or chaotic chirping through convective deformation of resonant phase-space structures. When drag is combined with diffusion or Krook relaxation, clear transition sequences emerge: increasing drag breaks hole-clump symmetry, broadens the effective resonance region, and drives systematic transitions from transient to intermittent and persistent chirping. At fixed ratios of collision operators, higher absolute collision rates require larger wave amplitudes to balance collision-driven restoration against wave-induced phase-space flattening. Furthermore, extending our analysis into linearly stable regimes reveals robust subcritical nonlinear behavior, where finite-amplitude initial perturbations overcome background dissipation to trigger nonlinear states. These results provide unified nonlinear regime maps and mechanistic phase-space interpretations for energetic-particle-driven chirping, offering a predictive framework that is directly relevant to the diagnosis and control of chirping Alfv & eacute;nic activity in fusion experiments.

Energetic electrons significantly influence power coupling and transport in helicon plasmas. Although energetic electrons and Landau damping processes have been reported in previous helicon studies, their nonlinear interaction with waves and the resulting saturation dynamics have not been quantified. Here, we present the first self-consistent analysis of the bump-on-tail (BOT) instability in helicon discharges using the BOT model adapted to helicon-relevant parameters. Under experimental conditions, the instability exhibits weakly nonlinear growth and saturates without frequency chirping, resulting from the balance between energetic-electron drive and Krook-type collisional relaxation. Parameter scans show that collisionality plays a dual role-damping the wave while continually repopulating the resonant velocity region-leading to enhanced saturation amplitude and stronger modifications to the electron distribution. Increasing the energetic drive further intensifies the nonlinear wave-particle coupling and broadens the plateau in velocity space. By coupling the BOT-induced electric field to fluid and Poisson equations, we show that the resulting density and flux perturbations can be an order of magnitude larger in rotating plasmas than in stationary ones. The model thus reveals a kinetic-to-fluid coupling pathway, showing that resonant electrons can modify macroscopic transport and power deposition. These results advance the understanding of wave-particle interaction in high-density radio frequency (RF) plasmas and provide a physics basis for optimizing power coupling and stability in next-generation helicon devices.

Helicon plasma sources play a central role in applications ranging from material treatment to space propulsion and fusion, yet the physical processes governing their ignition and transient ionization remain incompletely understood. Here we develop a self-consistent, fully coupled multiphysics framework implemented in COMSOL Multiphysics, that integrates Maxwell's equations, electron energy transport, drift-diffusion kinetics, and heavy-species chemistry to capture the complete spatiotemporal evolution of helicon discharges. The model reproduces experimental measurements across pressure, magnetic field, and frequency ranges, and reveals a previously unresolved transient ionization stage characterized by a rapid density rise within ~ 10- 4 s, accompanied by a two-peak electron temperature structure that governs the formation of the dense plasma core. By tracking the RF power flow and field topology, we characterize the transient redistribution of RF energy during ignition. A short-lived phase of localized energy deposition accompanies the onset of ionization, followed by a gradual restructuring of the RF field distribution as the plasma density increases, together with rapid density growth and profile restructuring. Systematic parametric scans further reveal the sensitivity of this mode-coupling process to gas pressure, magnetic field strength, and driving frequency. These results provide a unified picture of the ignition in helicon plasmas and establish a predictive tool for the design and optimization of RF plasma sources across space propulsion, manufacturing, and fusion technologies.

The spatial and temporal evolutions of blue-core helicon discharge driven by a planar antenna with four concentric rings are explored on the Linear Experimental Advanced Device (LEAD). The discharge experiences distinct density jumps from E mode to H mode, W mode, and blue-core mode, when RF input power increases. This is similar to previous observations using other typical helicon antennas; however, this special antenna could drive modes of even higher levels for which the blue-core plasma column is actually hollow in radius, i.e. peaking off-axis, which was not presented before. The column shows counterclockwise rotation for blue-core mode and clockwise rotation for non-blue-core mode. The reason could be attributed to the radial electric field differenceses for both modes which reverses the rotation direction via ExB drive. Moreover, the centrifugal instability of blue-core helicon plasma is computed using a two-fluid flowing plasma model. It shows that the instability is strong for small axial wave number but becomes weak for large axial wave number. Perturbed density peaks at radius of 0.045 m, while the equilibrium density gradient peaks at radius of 0.055 m. The coincidence of their radial locations suggests that it is a resistive drift mode driven by density gradient. The blue-core mode weakens once the magnetic field or flow rate exceeds the threshold value. Increasing power further leads to a smoother plasma density gradient. The electron temperature profiles decrease with increased power, and the radial gradient of the electron temperature inside the core is smaller as the magnetic field changes. To our best knowledge, it is the first detailed characterization of blue-core helicon plasma driven by planar antenna, especially in terms of azimuthal rotation and centrifugal instability.

We investigate the spatial and temporal dynamics of blue-core helicon discharge using a novel planar antenna with four concentric rings on the LEAD (Linear Experimental Advanced Device, JINST 15: P11002, 2020). As RF power increases, the discharge transitions through E, H, W, and blue-core modes at 1100 W, exhibiting a hollow density profile peaking off-axis. High-speed imaging reveals counterclockwise rotation in the blue-core mode (800 rad/s at 2000 W), contrasting with clockwise rotation in non-blue-core modes, driven by a radial electric field reversal. A two-fluid flowing plasma model predicts a centrifugal instability that is strongest at small axial wavenumbers, weakening as the wavenumber increases. The blue-core mode diminishes beyond thresholds of 2.0 Pa or 800 G. This study highlights unique density profiles and rotational dynamics, advancing the understanding of helicon plasma behavior.

The frequency dependence of the energy and ion current at the output of an RF plasma source with SPT geometry has been investigated. It has been shown that the ion energy is maximum when operating at a frequency of 6.8 MHz. An increase in the operating frequency is accompanied by a decrease in ion energy. The ion current depends nonmonotonically on frequency. At frequencies less than 27.12 MHz, an increase in the ion energy is accompanied by a decrease in the current, and a decrease in the energy by an increase in the current. Increasing the frequency to 27.12 MHz does not lead to an increase in the ion current.

This work explores for the first time bump-on-tail (BOT) instability excited by energetic electrons in helicon plasma. The Berk-Breizman model that developed for the wave-particle interaction and resulted instability in magnetic fusion is used. Details of the BOT instability are computed referring to typical helicon discharge conditions. Parameter studies are also conducted to reveal the effects of collisionality and energetic drive, to account for high-pressure and high-power senarios respectively. It is found that under the HXHM (high magnetic field helicon experiment) experimental parameters, the disturbed distribution function oscillates explosively at the initial stage of BOT instability excitation, and the wave frequency shift does not appear, i.e., the steady-state solution always exists under this mode. In the process of restoring stability, the exchange of energetic particles and wave energy is concurrent with the change of wave amplitude. As the Krook operator increases (i.e., from 0.1 to 1), the saturation level of the electric field and the instability enhance. Additionally, there have a bigger disturbance for the initial EEDF (electron energy distribution function) in high-power helicon devices, so that the energy exchange between waves and energetic particles is stronger as well. Moreover, BOT instability effects the density and flux of bulk plasma, and the flux increases with the Krook operator. The effect of BOT instability is one order of magnitude larger on rotating plasma than that on stationary plasma.These findings present a full picture of BOT instability in helicon plasma and are valuable to controlling it for efficient and safe applications, e.g., high-power space plasma propulsion and plasma material interactions using helicon source.

In this work, we carried out studies of the properties of an inductive RF discharge placed in a magnetic field with an induction of less than 70 G at frequencies of 2, 4 and 13.56 MHz. Experiments have shown that when operating at frequencies of 2 and 4 MHz at low powers of the RF generator, the range of existence of the discharge is limited by large magnetic fields. The efficiency of RF power input η non-monotonically depends on the magnitude of the magnetic field. The position of the main maximum η shifts to the region of higher B with increasing frequency, power of the RF generator and argon pressure, and at the same time the maximum broadens. An increase in frequency, power and argon pressure is accompanied by an increase in the absolute values of η. When operating at a frequency of 4 MHz, in addition to the main maximum η, a local maximum appears in the region B 35–70 G. With increasing pressure, a shift in the position of the local maximum and its smoothing is observed. Comparison of experimental data with calculated data allows us to conclude that the local maximum of plasma density observed at weak magnetic fields is associated with resonant excitation of waves in the plasma source. At a frequency of 2 MHz, the excited wave is close to a transverse helicon, and at a frequency of 13.56 MHz, its properties approach the Trivelpiece–Gold wave.

The work presents the results of an experimental study of the characteristics of the RF capacitive discharge placed in a magnetic field with a predominant radial component. The experiments are performed in the plasma source, which has the geometry of a Hall thruster. The integrated characteristics of the discharge, as well as the axial distribution of the probe ion current in the channel of the plasma source, are measured using three diagrams of the organization of the external discharge circuit: with the open for DC discharge circuit, as well as in the combination of a capacitive discharge with a direct current discharge. The main measurements are made in the argon in the flowrate range of 0.75–1.8 mg/s and the power of the generator 80–300 W at a frequencies of 2, 4, and 13.56 MHz, the induction of the magnetic field lying in the range of 100–300 G. Evaluation of the parameters of the plasma engine based on capacitive RF discharge when working in air, argon and krypton are made.

The properties of an inductive RF discharge placed in a longitudinal external magnetic field with an induction of less than 70 G at frequencies of 2, 4, and 13.56 MHz are studied. The dependences of the region of existence of the discharge, the efficiency of the RF power input and the structure of the RF magnetic field on the external magnetic field induction are studied experimentally. The experimental results are compared with calculations based on a previously developed electromagnetic discharge model. It is shown that the local maximum of the plasma density observed at weak magnetic fields is associated with the resonant excitation of waves in the plasma source. The excited wave is close to a transverse helicon at a frequency of 2 MHz, and its properties approach the Trivelpiece–Gould wave at a frequency of 13.56 MHz,.

The article presents the results of an experimental study of the characteristics of a low-power helicon ion source. Particular attention is paid to the parameters of the particle flow emerging from the source and the possibilities for increasing ion energy. It was found that the voltage drop at the output of the source is small (10-15 V), and the main voltage drop is localized at the grounded elements. The ion flux density non-monotonically depends on the magnetic field, while the ion energy remains constant. Applying a constant voltage to the additional electrode inside the discharge chamber does not increase the potential drop at the output of the source. Switching to a lower operating frequency or narrower output orifices allows increasing ion energy, but leads to a decrease in ion flux. At the exit from the source, in the presence of a magnetic field, a directed flow of electrons was detected, the energy of which increases significantly with increasing magnetic field induction. The presence of wave processes in the discharge chamber, which may be responsible for the appearance of an accelerated electron flow, has been demonstrated.

The parameters of a radio-frequency capacitive discharge confined in a closed electron drift accelerator with an extended acceleration zone have been studied for different discharge circuits, namely, with dc-closed and dc-open electrodes and with additional dc biasing of the active electrode. In the open circuit, the plasma concentration is minimal and the ion energy in the jet at the exit from the prototype is about 25 eV. The dc closing of the active electrode increases both the plasma density and the ion energy to 250 eV. A further increase or decrease in these parameters is possible by applying a positive or negative dc bias, respectively, to the active electrode.

A pulsed RF discharge is considered experimentally as a working process of an RF ion source. It is shown that an increase in the ion current can be obtained in comparison with the continuous operation mode when such a discharge is operating. This increase is the greater, the greater the difference between the characteristic time of the drop of the ion current after turning off the RF power and the rise time of the ion current when the RF power is turned on. The pulsation parameters at which the ion current is maximized are estimated. It is shown that an external constant longitudinal magnetic field in the range of 0–7.2 mT nonmonotonically affects the maximum and equilibrium value of the ion current in a pulse and does not affect the decrease rate of the ion current after the RF power is turned off.

The results of an experimental study of a low-power RF plasma source placed in a longitudinal magnetic field (helicon thruster), when it operates on a capacitive RF discharge and inductive RF discharges with a capacitive component, are presented. A significant dependence of the characteristics of the ion and electron fluxes of the source on the induction of a constant magnetic field is shown. The fundamental applicability of capacitive RF discharge as a working process in the studied plasma source is demonstrated. It is shown that the increase in the average energy of ions in the flow at the outlet of the source with the appearance of the capacitive component of the discharge is slight.

The paper describes an experimental study of the characteristics of a pulse-modulated radio-frequency(RF)discharge sustained at low pressures,typical of the operating modes of RF gridded ion sources.The motivation for the study is the question of whether the RF pulse-modulated mode can increase the efficiency of the ion source.The ion current values extracted from an RF inductive ion source operating in continuous and pulse-modulated modes were compared.The experimental data were also compared with the parameter calculations based on a 0D numerical model of the discharge.The measurements showed that the pulse-modulated operation mode of the RF ion source had a noticeable advantage when the power of the RF generator was 140W or lower.However,as the generator power increased,the advantage was lost because the pulse-modulated operation mode,having a higher RF power instant value,entered the region of existence sooner than the continuous mode,where the ion production cost begins to grow with RF power.

The work presents the results of an experimental study of the characteristics of the RF capacitive discharge placed in a magnetic field with a predominant radial component. The experiments are performed in the plasma source, which has the geometry of a Hall thruster. The integrated characteristics of the discharge, as well as the axial distribution of the probe ion current in the channel of the plasma source, are measured using three diagrams of the organization of the external discharge circuit: with the open for DC discharge circuit, as well as in the combination of a capacitive discharge with a direct current discharge. The main measurements are made in the argon in the flowrate range of 0.75 - 1.8 mg/s and the power of the generator 80 - 300 W at a frequencies of 2, 4 and 13.56 MHz, the induction of the magnetic field lying in the range of 100 - 300 G. Evaluation of the parameters of the plasma engine based on capacitive RF discharge when working in air, argon and krypton are made.

Экспериментально изучены параметры емкостного высокочастотного разряда, зажигаемого в геометрии ускорителя с замкнутым дрейфом электронов с протяженной зоной ускорения при различных схемах организации разряда, а именно, при разомкнутых и замкнутых по постоянному току электродax, а также при дополнительной подаче постоянного смещения на нагруженный электрод. В разомкнутой схеме реализуется минимальная концентрация плазмы, энергия ионов в струе на выходе из прототипа порядка 25 эВ. Замыкание по постоянному току нагруженного электрода увеличивает как плотность плазмы, так и энергию ионов до 250 эВ. Дальнейшее увеличение или уменьшение этих параметров возможно при подаче соответственно положительного или отрицательного постоянного смещения на нагруженный электрод.

The paper presents the results of an experimental study of the axial structure of the longitudinal RF magnetic field and parameters of the plasma of an inductive low-power plasma source placed in a magnetic field of 12–72 G. It is shown that, already in a magnetic field of 24 G, a nonmonotonic dependence of the longitudinal component of the RF magnetic field on the axial coordinate is clearly manifested. The change in the phase of the RF field indicates that a partially traveling wave is formed in the discharge. Probe measurements show that the electron energy distribution function is enriched with fast electrons whose velocity correlates with the phase velocity of the wave.

The present work aims to analyze the mutual influence of channels in a combined discharge based on the RF inductive and DC discharges and to find the conditions under which the gain in the plasma density can be obtained. A cylindrical plasma reactor with a diameter of 20 cm and a length of 20 cm has been used as an object of research. The measurements have been carried out in argon at pressures of 0.08 and 8 Pa, as well as in air at pressures of 8 and 18.7 Pa. The performed experiments have shown that the gain in plasma density in the combined discharge is possible under conditions when the plasma density in DC discharge overcomes that in the inductive one. As a rule, such situation occurs when inductive discharge is in a E-mode. Due to the higher value of the plasma density, provided by the DC channel, the RF power input through the inductive discharge increases. A synergistic effect appears, and the resulting plasma density exceeds the sum of the densities, specific to the inductive and DC discharges separately.