Mirror Trap Research Articles

1D drift-kinetic numerical model based on semi-implicit particle-in-cell method

The paper presents a new one-dimensional drift-kinetic electrostatic model based on the particle-in-cell method and capable of simulating the processes of plasma heating and confinement in mirror traps. The most of particle and energy losses in these traps occur along the magnetic field lines. The key role in limiting these losses is played by the ambipolar electric potential which creates a potential barrier for electrons and significantly reduces the heat flux that, without this barrier, would go to wall due to the classical electron thermal conductivity. However, modeling the formation of such a potential on real spatial and temporal scales of experiments is a challenging problem, since it requires a detailed description of not only ion, but also electron kinetics. In this work, we propose to solve the problem of taking into account electron kinetic effects on the time scale of plasma confinement in a mirror trap using the particle-in-cell method adapted to the approximate drift-kinetic equations of plasma motion. Unlike other electrostatic particle-in-cell models, which use fully implicit schemes to solve the nonlinear system of Vlasov-Poisson and Vlasov-Ampere equations, we propose a semi-implicit approach. By analogy with the Energy Conserving Semi-Implicit Method (ECSIM), it allows for precise conservation of energy and reduces the procedure for finding the electric field to inverting a tridiagonal matrix without multiple nonlinear iterations. Such a model will be useful for simulating not only collisional losses of hot plasma in fusion experiments, but also for studying the features of creating cold starting plasma in mirror traps using plasma or electron guns.

Influence of the shape of a conducting chamber on the stability of rigid ballooning modes in a mirror trap

MHD stabilization of flute and ballooning modes in an axisymmetric mirror trap is studied under the assumption of strong finite Larmor radius effect that suppresses all perturbations with azimuthal numbers m⩾2 and makes the m = 1 mode ‘rigid’. The rigid mode can be effectively suppressed using perfectly conducting lateral wall without any additional means of stabilization or in combination with end MHD anchors. Numerical calculations were carried out for an anisotropic plasma produced in the course of neutral beam injection into the minimum of the magnetic field at the right angle to the trap axis. The stabilizing effect of the conducting shell made of a straightened cylinder is compared with a proportional chamber, which, on an enlarged scale, repeats the shape of the plasma column. It is confirmed that for convincing wall stabilization of the rigid modes, the plasma beta (β, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value βcr2 . When conducting lateral wall is combined with conducting end plates imitating MHD end anchors, there are two critical betas and, respectively, two stability zones β<βcr1 and β>βcr2 that can merge, making the entire range 0<β<1 of betas allowable for stable plasma confinement. The dependence of the critical betas on the plasma anisotropy, mirror ratio, width of the vacuum gap between the plasma column and the lateral wall, radial pressure profile and the axial magnetic field profile is examined.

A compact microfluidic laser-induced fluorescence immunoassay system using avalanche photodiode for rapid detection of alpha-fetoprotein.

Alpha-fetoprotein (AFP), commonly employed for early diagnosis of liver cancer, serves as a biomarker for cancer screening and diagnosis. Combining the high sensitivity and specificity of fluorescence immunoassay (FIA), developing a low-cost and efficient immunoassay system for AFP detection holds significant importance in disease diagnosis. In this work, we developed a miniaturized oblique laser-induced fluorescence (LIF) immunoassay system, coupled with a microfluidic PMMA/paper hybrid chip, for rapid detection of AFP. The system employed an avalanche photodiode (APD) as the detector, and implemented multi-level filtering in the excitation light channel using the dichroic mirror and optical trap. At first, we employed the Savitzky-Golay filter and baseline off-set elimination methods to denoise and normalize the original data. Then the cutoff frequency of the low-pass filter and the reverse voltage of the APD were optimized to enhance the detection sensitivity of the system. Furthermore, the effect of laser power on the fluorescence excitation efficiency was investigated, and the sampling time during the scanning process was optimized. Finally, a four-parameter logistic (4PL) model was utilized to establish the concentration-response equation for AFP. The system was capable of detecting concentrations of AFP standard solution within the range of 1-500 ng/mL, with a detection limit of 0.8 ng/mL. The entire immunoassay process could be completed within 15 min. It has an excellent potential for applications in low-cost portable diagnostic instruments for the rapid detection of biomarkers.

On the Existence of Global Compactly Supported Weak Solutions of the Vlasov–Poisson System with an External Magnetic Field

We consider the first mixed problem for the Vlasov–Poisson system with an external magnetic field in a domain with piecewise smooth boundary. This problem describes the kinetics of a two-component high-temperature plasma under the influence of a self-consistent electric field and an external magnetic field. The existence of global weak solutions is proved. In the case of a cylindrical domain, sufficient conditions are obtained for the existence of global weak solutions with supports in a strictly internal cylinder; this corresponds to the confinement of high-temperature plasma in a mirror trap.

Numerical Simulation of the Spatial Structure of the Electromagnetic Field of a Microwave Discharge in a Magnetic Mirror Trap

Numerical Simulation of the Spatial Structure of the Electromagnetic Field of a Microwave Discharge in a Magnetic Mirror Trap

The role of electron current in high-β plasma equilibria

This paper is aimed at investigating the role of electrons in creation of currents in plasma equilibria with high plasma pressure (β≈1). Despite the long history of studies of these equilibria, there is still no consensus on what kind of particle species is responsible for the creation of the diamagnetic current and what characteristic size the current layer should have. For example, simulations of isothermal plasma injection into a multi-cusp magnetic trap [J. Park et al., Front. Astron. Space Sci. 6, 74 (2019)] demonstrate the formation of a transition layer with a thickness comparable to the electron Larmor radius, where the equilibrium current is carried by electrons. At the same time, studies of a diamagnetic bubble created by a hot-ion plasma in a mirror trap [I. Kotelnikov, Plasma Phys. Control Fusion 62, 075002 (2020)] assume ion dominance and completely ignore electron currents. In this paper, we show that the equilibrium initially governed by the ion diamagnetic current is unstable against perturbations at the ion-cyclotron frequency harmonics, and this instability forces the plasma to come to a new equilibrium state in which the current is mainly created by the E×B-drift of electrons. The same type of equilibrium is also found to form in a more realistic problem setup when plasma is continuously injected into the uniform vacuum magnetic field.

Wall stabilization of high-beta anisotropic plasmas in an axisymmetric mirror trap

The stabilization of the ‘rigid’ flute and ballooning modes both with and without the effect of additional MHD anchors in an axisymmetric mirror trap, with the help of a perfectly conducting lateral wall, is studied using a model pressure distribution of a plasma with a steep-angle neutral beam injection at the magnetic field minimum. The calculations were performed for an anisotropic plasma in a model that simulates the pressure distribution during the injection of beams of fast neutral atoms into the magnetic field minimum. It is assumed that the lateral wall is an axisymmetric shell surrounding the plasma that follows the shape of the magnetic field line and is placed at a certain distance to the plasma border. It has been found that for the effective stabilization of the modes by the lateral wall only the parameter beta (β, ratio of plasma pressure to the magnetic field pressure) must exceed some critical value β crit. When combined with the conducting end plates imitating the MHD end stabilizers, there are two critical beta values and two stability zones and that can merge, making the entire range of allowable beta values stable. The dependence of the critical betas on the degree of plasma anisotropy, the mirror ratio, and the width of the vacuum gap between the plasma and the lateral wall is studied. In contrast to the previous studies focusing on a plasma model with a sharp boundary, we calculated the stability zones for a number of diffuse radial pressure profiles and several axial magnetic field profiles.

High-Efficiency Plasma Source Using a Magnetic Mirror Trap for Miniature-Ion Pumps

In this study, we design a highly efficient plasma source using a magnetic mirror trap with two opposing permanent magnets for a miniature high-efficiency ion pump. First, we simulated the distribution of the magnetic field line formed by the proposed magnetic mirror configuration. By optimizing the distance between two opposing permanent magnets and size of these magnets, a magnetic mirror ratio value of 27 could be obtained, which is an electron confinement efficiency of over 90%. We also conducted an experiment on a high-efficiency discharge plasma source for a miniature ion pump using an optimized magnetic circuit. As a result, we revealed that the proposed magnetic circuit has a pronounced effect on plasma generation, particularly in the high-vacuum region.

Wall stabilization of the rigid ballooning m = 1 mode in a long-thin mirror trap

The prospect of stabilization of the m = 1 ‘rigid’ ballooning mode in an open axially symmetric long-thin trap with the help of a conducting lateral wall surrounding a column of isotropic plasma is studied. It was found that for effective wall stabilization, the beta parameter β must exceed some critical value β crit. The dependence of β crit on the mirror ratio, radial pressure profile, axial profile of the vacuum magnetic field, and the width of vacuum gap between plasma and lateral wall was studied. Minimal critical beta at the level of 70% is achieved at zero vacuum gap, although stability zone at β → 1 exists even at extremely wide vacuum gap. It is shown that when a conducting lateral wall is combined with conducting end plates simulating attachment of the end MHD stabilizers to the central cell of an open trap, there are two critical beta values and two stability zones that can merge, making stable the entire range of allowable beta values 0 < β < 1.

Electron beam-plasma discharge in GDT mirror trap: experiments on plasma start-up with electron gun

The paper describes experiments on the injection of an electron beam into a gas at the gas dynamic trap (GDT) and develops a technique for creating a starting plasma with parameters sufficient for its subsequent heating by neutral beams. It is found that a relatively thin electron beam is capable of ionizing plasma in the entire volume of the trap, and the plasma turbulence it excites is capable of accelerating some of the electrons to energies tens of times higher than the initial energy of the beam. It is shown that, in contrast to early experiments on tabletop open traps, collective beam relaxation under GDT conditions occurs in the vicinity of the entrance magnetic mirror. Since the electron cyclotron frequency in this region significantly exceeds the plasma frequency, it is necessary to study the mechanism of a beam-plasma discharge under these conditions. As a first step along this path, we measure the radial diffusion coefficient of fast particles, as well as the rate at which they gain energy.

Energy distribution and bremsstrahlung spectra of energetic electrons escaping from the ECR plasma with high energy input

Electron energy distribution function (EEDF) is an important characteristic that defines the processes of plasma confinement and ionization. Understanding such processes is crucial for the proper tuning of ion sources. In the ECR plasma, the EEDF is significantly non-Maxwellian, and the exact shape remains still unknown. As the initial step towards the EEDF resolving, the energy distribution of the electrons lost from the magnetic mirror trap was directly measured in a wide range of neutral gas pressures and gyrotron powers along with bremsstrahlung spectra. A series of experiments were performed on the newly constructed Gasdynamic Ion Source for Multipurpose Operation (GISMO) facility allowing record-breaking specific energy input into the plasma. Obtained distributions showed unconventional behavior as the function of source parameters. The EEDF shape and the bremsstrahlung spectra showed a threshold qualitative change with the gyrotron power presumably as a result of the development of kinetic instabilities.

High power vacuum ultraviolet source based on gasdynamic ECR plasma

We report experimental results of vacuum ultraviolet (VUV) emission from the plasma of an electron cyclotron resonance (ECR) discharge in hydrogen, sustained by millimeter-wavelength radiation of a gyrotron. The considered discharge is characterized with the high plasma density (1013 cm−3 order of magnitude) and, at the same time, the high electron average energy (10–300 eV), which makes it possible to significantly increase the efficiency of VUV re-emission of the energy deposited into the plasma by the microwave radiation. Experiments were performed with the plasma confined in a simple mirror trap and heated by pulsed gyrotron radiation of 37.5 GHz/100 kW under the ECR condition. The measured volumetric VUV emission power of Lyman-alpha line (122 10 nm) overlapping with the Werner band, Lyman band (160 10 nm), and molecular continuum (180 20 nm) reached 45, 25, and 55 W/cm3, respectively. The total absolute radiation power in these three ranges integrated over the plasma volume is estimated to be 22 kW, i.e., 22% of the incident microwave power, which matches theoretical predictions. The development of effective technological VUV sources of a kilowatt power level is expected to be the next step following the optimization of the conditions of the ECR hydrogen discharge sustained by powerful gyrotron radiation.

On the stability of small-scale ballooning modes in axisymmetric mirror traps

It is shown that a steepening of the radial plasma pressure profile leads to a decrease in the critical value of beta, above which, small-scale balloon-type perturbations in a mirror trap become unstable. This may mean that small-scale ballooning instability leads to a smoothing of the radial plasma profile. The critical beta values for the real magnetic field of the gas-dynamic trap and various plasma pressure radial profiles was also calculated. For a plasma with a parabolic profile critical beta is evaluated at the level of 0.72. A previous theoretical prediction for this trap was almost two times lower than maximal beta 0.6 achieved experimentally.

Optimization of power matching and transfer in the helicon plasma discharge

Helicon plasma source is being developed at the Budker Institute of Nuclear Physics SB RAS, Novosibirsk. The parameters are studied of the plasma confined in a mirror trap configuration of the magnetic field at an operating frequency of 13.56 MHz. For matching the antenna impedance and generator load, the Π-type matching box was designed and successfully tested at powers of 20–25 kW. The low reflected power (1–2%) was obtained, as compared to that for the L-type matching network used previously (the reflected power was more than 15% at the generator output power of 18 kW). The triple Langmuir probe is used to determine the plasma density. The plasma resistive characteristics were determined using the Rogowski coil measuring the RF antenna current. In the experiments, the plasma with a density of ∽5⋅1012 cm-3 and an electron temperature on axis of 10 eV was obtained, and the RF power transfer efficiency was ∽85% at the RF power of 25 kW.

Long-pulse plasma source for SMOLA helical mirror

A plasma gun for forming a plasma stream in the open magnetic mirror trap with additional helicoidal field SMOLA is described. The plasma gun is an axisymmetric system with a planar circular hot cathode based on lanthanum hexaboride and a hollow copper anode. The two planar coils are located around the plasma source and create a magnetic field of up to 200 mT. The magnetic field forms the magnetron configuration of the discharge and provides a radial electric insulation. The source typically operates with a discharge current of up to 350 A in hydrogen. Plasma parameters in the SMOLA device are Ti ~ 5 eV, Te ~ 5–40 eV and ni ~ (0.1–1) × 1019 m−3. Helium plasma can also be created. The plasma properties depend on the whole group of initial technical parameters: the cathode temperature, the feeding gas flow, the anode-cathode supply voltage and the magnitude of the cathode magnetic insulation.

A general way to confined stationary Vlasov-Poisson plasma configurations

We address the existence of stationary solutions of the Vlasov-Poisson system on a domain $\Omega\subset\mathbb{R}^3$ describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a subregion of $\Omega$. In a first part we provide such an existence result for a generalized system of Vlasov-Poisson type and investigate the relation between the strength of the external magnetic field, the sharpness of the confinement and the amount of plasma that is confined measured in terms of the total charges. The key tools here are the method of sub-/supersolutions and the use of first integrals in combination with cutoff functions. In a second part we apply these general results to the usual Vlasov-Poisson equation in three different settings: the infinite and finite cylinder, as well as domains with toroidal symmetry. This way we prove the existence of stationary solutions corresponding to a two-component plasma confined in a Mirror trap, as well as a Tokamak.

Panopticon: not a Transformer, but transforming ion trapping technology

A combination of a hemispherical mirror and unique ion trap design allows for the observation of quantum electrodynamics effects in complex systems.

Simulations of fusion neutron source based on the axially symmetric mirror trap for the thorium hybrid reactor

The axially symmetric open mirror trap is considered as a neutron source for the hybrid thorium reactor. Plasma parameters are optimized in order to achieve the maximum neutron yield in the volume surrounded by the subcritical fuel assembly while meeting the stability criteria. For plasma consisting of equal amounts of deuterium and tritium isotopes, in the fuel assembly region, the neutron yield was found to be 0.6 × 1017 n/s at an input power of 20 MW, and it will increase to 2.6 × 1017 n/s if the input power increases two times. In optimal regimes, the plasma parameters were close to those achieved in experiments at the GDT facility.

Neutron data field in a fission reactor core with fusion neutron source at pulse-periodic operation

Results are presented on the distinctive features of the energy release dynamics in the hybrid thorium reactor operating in combination with the neutron source based on the extended magnetic mirror trap. In the reactor core configuration under study, the high-temperature plasma column is formed in a pulse-periodic mode. At a certain duty cycle (pulse ratio) of the plasma column formation, it can be expected that the fission “wave” will be formed diverging from the axial region of the system and propagating in the radial direction in the fuel assembly (blanket). Under such conditions, in order to correct the resulting offset of the energy release distribution, it is necessary to optimize the fuel composition of the assembly in order to obtain the most appropriate radial distributions of physical parameters. The studies are carried out on the basis of the full-scale model of the reactor core, in which the axial region is modified: the extended magnetic mirror trap operating as a source of fusion neutrons is installed in the reactor core axial region.

Simulations of parameters of the mirror trap-based neutron source limited by the development of DCLC instability

The axially symmetric mirror trap with deuterium-tritium plasma is considered as a neutron source for the hybrid reactor. The goal of this study is to select the facility parameters, providing the maximum neutron yield at a fixed input power. The procedure is proposed for verifying the sufficient criterion for stability of the drift-cone ion-cyclotron mode. Within a limited set of configurations under consideration, the maximum fusion reaction power of 5.8 MW is achieved at an input power of 100 MW.