An overview of the neutral beam injectors developed at the Budker Institute of Nuclear Physics in Novosibirsk during the last 10 years is presented. These neutral injectors are used for plasma diagnostics, heating and current drive in modern fusion devices with magnetic confinement. An arc or a radio-frequency (RF) discharge generates a plasma in the ion sources of the injectors, and a positive hydrogen or deuterium ion beam is extracted and accelerated by a multiaperture ion-optical system (IOS). The accelerated ion beam is converted into a neutral one in a gas target. The precision multiaperture IOS with spherically concave electrodes provides ballistic focusing of the neutral beam. The high-energy, high-power beam injector based on negative ions, which is currently under development, is described as well. It comprises a RF negative ion source and a wide-aperture electrostatic accelerator separated from the source by a low-energy beam transport line, thereby improving the injector reliability.

The paper presents experimental results from the SMOLA device that is the first facility with a helical mirror section of the magnetic field. This device is built in the Budker Institute of Nuclear Physics for the verification of the helical mirror confinement idea that is the recently introduced technique of the active control of axial losses from a confinement zone. Theory predicts that with rotating plasma, a helical mirror will provide suppression of the axial plasma flow and, simultaneously, density pinching to the axis. Experiments demonstrated that plasma density at the exit from the transport section is suppressed with activation of the helical field, the effect is significant and highly reproducible. The most pronounced effect is observed on the plasma periphery, where the mirror ratio is the highest. The integral suppression ratio reaches 2–2.5 in the discussed experiments. Experimental results are compared with simplified theoretical estimates. The integral suppression ratio matches the simple theoretical estimates even if the transversal diffusion is neglected.

The paper presents experimental results from the SMOLA device on the testing of the helical mirror confinement hypothesis. Helical mirror confinement is the technique of an active control of axial plasma losses from a confinement zone by multiple magnetic mirrors that move along the axis in the reference frame of the plasma that experiences $\boldsymbol{E} \times \boldsymbol{B}$ rotation due to an applied radial electric field. Theory predicts that a helical mirror will provide an axial force that modifies the plasma flow and, simultaneously, density pinching to the axis. The force direction depends on the plasma rotation direction. Experimental data on the axial plasma losses at different direction of the magnetic mirror movement are presented. If the trapped ions move in the direction opposite to the direction of the axial losses, then the particle flux reduces in the broad range of the plasma density. The confinement improves with the increase of the fraction of the trapped particles (effective mirror ratio was up to $R_{{\rm eff}}=5.8\pm 1.4$). If the trapped ions move in the same direction as the axial losses, then the flux depends on density. At intermediate densities, the integral flux through the transport section rises compared to the plasma flowing through the straight magnetic field. The effective mirror ratio is lower and does not significantly depend on the fraction of the trapped particles (effective mirror ratio at intermediate density was $R_{{\rm eff}}=3.3\pm 0.8$).

The centrifugal mirror confinement scheme incorporates supersonic rotation of a plasma into a magnetic mirror device. This concept has been shown experimentally to drastically decrease parallel losses and increase plasma stability as compared with prior axisymmetric mirrors. MCTrans++ is a dimensionless (0-D) scoping tool which rapidly models experimental operating points in the Centrifugal Mirror Fusion Experiment (CMFX) at the University of Maryland. In the low-collisionality regime, parallel losses can be modelled analytically. A confining potential is set up that is partially ambipolar and partially centrifugal. Due to the stabilizing effects of flow shear, the perpendicular losses can be modelled as classical. Radiation losses such as bremsstrahlung and cyclotron emission are taken into account. A neutrals model is included, and, in some circumstances, charge-exchange losses are found to exceed all other loss mechanisms. We use the SUNDIALS ARKODE library to solve the underlying equations of this model; the resulting software is suitable for scanning large parameter spaces, and can also be used to model time-dependent phenomena such as a capacitive discharge. MCTrans++ has been used to verify results from prior centrifugal mirrors, create an experimental plan for CMFX and find configurations for future reactor-scale fusion devices.

The Wisconsin high-temperature superconductor axisymmetric mirror experiment (WHAM) will be a high-field platform for prototyping technologies, validating interchange stabilization techniques and benchmarking numerical code performance, enabling the next step up to reactor parameters. A detailed overview of the experimental apparatus and its various subsystems is presented. WHAM will use electron cyclotron heating to ionize and build a dense target plasma for neutral beam injection of fast ions, stabilized by edge-biased sheared flow. At 25 keV injection energies, charge exchange dominates over impact ionization and limits the effectiveness of neutral beam injection fuelling. This paper outlines an iterative technique for self-consistently predicting the neutral beam driven anisotropic ion distribution and its role in the finite beta equilibrium. Beginning with recent work by Egedal et al. (Nucl. Fusion, vol. 62, no. 12, 2022, p. 126053) on the WHAM geometry, we detail how the FIDASIM code is used to model the charge exchange sources and sinks in the distribution function, and both are combined with an anisotropic magnetohydrodynamic equilibrium solver method to self-consistently reach an equilibrium. We compare this with recent results using the CQL3D code adapted for the mirror geometry, which includes the high-harmonic fast wave heating of fast ions.

This paper explores the feasibility of a break-even-class mirror referred to as BEAM (break-even axisymmetric mirror): a neutral-beam-heated simple mirror capable of thermonuclear-grade parameters and $Q\sim 1$ conditions. Compared with earlier mirror experiments in the 1980s, BEAM would have: higher-energy neutral beams, a larger and denser plasma at higher magnetic field, both an edge and a core and capabilities to address both magnetohydrodynamic and kinetic stability of the simple mirror in higher-temperature plasmas. Axisymmetry and high-field magnets make this possible at a modest scale enabling a short development time and lower capital cost. Such a $Q\sim 1$ configuration will be useful as a fusion technology development platform, in which tritium handling, materials and blankets can be tested in a real fusion environment, and as a base for development of higher-$Q$ mirrors.

The paper presents an investigation of the plasma fluctuation in the SMOLA helical mirror, which is suspected to be responsible for anomalous scattering. The helical mirror confinement is effective when the ion mean free path is equal to the helix pitch length. This condition can be satisfied in hot collisionless plasma only by anomalous scattering. The wave, which scatters the passing ions, is considered to receive energy from the trapped ions. The oscillations of the electric field in the helically symmetric plasma were observed in experiment. The oscillations have both regular highly correlated and chaotic components. The dependency of the regular component frequency on the Alfvén velocity is linear for $V_{\rm A} < 2.8 \times 10^6\ \text {m}\ \text {s}^{-1}$ and constant for higher values. It is shown experimentally that the condition for the wave to be in phase resonance with the trapped ions is satisfied in a specific region of the plasma column for the highly correlated component. The amplitude of the chaotic component (up to $3\ \text {V}\ \text {cm}^{-1}$) is higher than the estimated electric field required for the ion scattering.

Influence of the local-ionization-induced neutral depletion on the thrust imparted by the magnetic nozzle plasma thruster is discussed by simply considering reduction of the neutral density due to the ionization in the thruster model combining the global source model and the one-dimensional magnetic nozzle model. When increasing the rf power, it is shown that the increase rate of the plasma density is reduced, while the electron temperature continues to increase due to a decrease in the neutral density. Since the major components of the thrust are originated from the electron pressures in the source and in the magnetic nozzle, the increase in the electron temperature contributes to the increase in the thrust in addition to the gradual density increase by the rf power. The model qualitatively predicts the reduction of the thruster efficiency by the neutral depletion for the high-power condition, compared with the constant neutral density model.

A new magnetic mirror machine named KAIMIR (KAIST mirror) has been designed and constructed at the Korea Advanced Institute of Science and Technology (KAIST) to study mirror plasma physics and simulate the boundary regions of magnetic fusion plasmas such as in a tokamak. The purpose of this paper is to introduce the characteristics and initial experimental results of KAIMIR. The cylindrical vacuum chamber has a length of 2.48 m and a diameter of 0.5 m and consists of three sub-chambers, namely the source, centre and expander chambers. A magnetic mirror configuration is achieved by electromagnetic coils with a maximum magnetic field strength of 0.4 T at the mirror nozzles and 0.1 T at the centre. The source plasma is generated by a plasma washer gun installed in the source chamber with a pulse forming network system. The typical discharge time is ~12 ms with a ~6 ms (1–7 ms) steady period. Initial results show that the on-axis electron density at the centre is 1019–20 m−3 and the electron temperature is 4–7 eV. Two parameters were varied in this initial phase, the source power and the mirror ratio, which is the ratio of highest to lowest magnetic field strength in the mirror-confined region. We observed that the increase of the electron density was mitigated for a source power above 0.2 MW. It was also found that the electron density increases almost linearly with the mirror ratio. Accordingly, the stored electron energy was also linearly proportional to the mirror ratio, similar to the scaling of the gas dynamic trap.

The paper presents an overview of experimental results of an investigation of different energy loss channels in the gas dynamic trap (GDT), which is a magnetic mirror plasma confinement device in the Budker Institute of Nuclear Physics. Energy losses along magnetic field lines are considered as well as losses onto radial limiters, which restrict the plasma column radius and provide its magnetohydrodynamic stability via the ‘vortex confinement’ mechanism. The losses along the field lines were measured using a set of pyroelectric bolometers on the plasma absorber and the losses onto the limiters were determined with thermistors from their temperature rise. Additionally, the losses due to charge exchange of fast plasma ions on the residual neutral gas in the GDT were measured using a longitudinal array of pyroelectric bolometers mounted on the wall of the central cell. An attempt was made to draw up the energy balance in the GDT in order to identify the predominant loss channels and reduce those losses in the future.

Collisionless charged particle motion and its transport in the two-wire model (TWM) with no axial magnetic fields is investigated numerically. The TWM configuration contains a magnetic X-point, and single particle motions in such a field have two conserved quantities: the total kinetic energy and the base field line value which is a quantity derived from the axial canonical momentum. As gyrating particles travel along the field lines, they may reach near the X-point region where the magnetic moment, the first adiabatic invariant, can be occasionally shifted due to a large gradient of the field. When the magnetic moment becomes large, resulting in a large Larmor radius, particles probabilistically cross the X-point to migrate to the opposite side of the TWM configuration. These phenomena are investigated with single particle simulations. We find that the statistical behaviour of the seemingly chaotic magnetic moment shifts are completely determined by the two aforementioned conserved quantities, and also that there exists a threshold energy, determined by the base field line value, allowing only particles with a higher energy to cross the separatrix and migrate. It is found that the crossing time is distributed exponentially, and that the migration confinement time, which is the average crossing time, is shorter for particles with a base field line closer to the separatrix and a higher energy. We provide an empirical expression, derived with the simulations, for estimating the collisionless migration confinement time.

A high-speed solenoid-type pulsed valve is applied to a water-fuelled magnetron sputtering thruster, which can lead a compact and neutralizer-free electric propulsion device by generating a thrust due to the ejection of the sputtered target material, in order to minimize the size of the gas feeding system. The pulsed valve is opened for approximately 5 msec and the gaseous water is introduced into the source via a gas line connected to the source. A dc high voltage is firstly applied between the cathode and the anode; then the discharge is sustained for the period in which a gas pressure enough for the discharge is maintained and a change in the discharge mode is observed during the discharge pulse. To investigate the impact of the mode change on the thrust generation, a temporally resolved measurement of the force is equivalently performed by installing a pulsed voltage power supply and by changing the pulse width of the discharge voltage. The results show the temporal reduction of the thrust-to-power ratio during a pulsed discharge due to the nonlinear correlation between ion energy and sputtering yield. It is suggested that the use of a pulsed valve would be useful for downsizing of the electric propulsion system, while an optimization to properly control the gas flow rate is needed for further development.

This paper is devoted to experimental studies of plasma confinement with high relative pressure ($\beta$) in the Gas Dynamic Trap (BINP, Novosibirsk). In previous high-$\beta$ confinement studies a maximum local $\beta = 0.6$ was achieved in the fast-ion turning point, contributed to by a beam-driven population of fast ions with an anisotropic distribution function. In this study the axial magnetic field profile was modified to bring the turning points closer to one another, which effectively increased the energy density of plasma and pushed the $\beta$ value higher. Experiments were performed for two non-standard magnetic configurations, where the axial fast-ion confinement region length was reduced by 1.5 and 2 times compared with the standard configuration. The average values of $\langle \beta _{\perp } \rangle$ over the plasma central cross-section were found to be 0.1 and 0.18, respectively, for the two configurations, with the latter value significantly exceeding the $\langle \beta _{\perp } \rangle =0.08$ of the standard configuration, in which the previous record was set. Moreover, halving the fast ion confinement region almost doubled the D–D fusion proton flux from the trap centre compared with the standard configuration. The electron temperature in both new magnetic configurations was only slightly smaller than in the standard configuration. In addition, an effect of Alfvén ion–cyclotron instability (AICI) development on the pressure in the turning points is discussed. Presumably, with some decrease in magnetic field an evolving AICI does not result in considerable pressure axial redistribution, so the pressure maximum is in the turning points’ vicinity despite the instability.

In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared with the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in $\lambda /L \ll 1$, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$, the electron inertial scale $d_e$ and the plasma $\beta$. This work is of general consequence in emphasising the fact that high-$\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta \gtrsim L/\lambda$. In this situation, the determination of transport coefficients via the standard CE approach is not valid.

A unique field-reversed configuration (FRC) experiment is presently being assembled at the Plasma Technology Research Institute, KFE. It is a compact small-scale FRC device, which uses a set of radio frequency (RF) antennas to produce an internal E × B that drives the electrons for current-drive, in which E is the electric field and B is the magnetic field. This is very similar to the rotating magnetic field (RMF) current-drive, where the horizontal and vertical antennas are driven 90° out of phase. For this device, the RF antennas are arranged differently than the RMF. The RF antennas, being two separate sets, are positioned inside the vacuum chamber. Each set consists of 8 coils, for a total of 16 coils, where 80~100 kHz sine and cosine waveform currents are applied. One set of coils generates a radial B-field, while the other set provides an E-field in the z-direction. As the phase changes, the E and B fields are switched by these two sets. Nevertheless, E × B propagates in the same θ-direction so that this allows the electrons to rotate around the circumference of the device. The FRC device will test wave heating by launching 2.45 GHz microwaves. Also, passive stabilizers are positioned at each end to provide extra stability while preventing tilt instability. The experiment is expected to produce its first plasma in 2025.