Mirror Ratio Research Articles

Improved axial confinement in the open trap by the combination of helical and short mirrors

The paper presents experimental results from the SMOLA device, which was built in the Budker Institute of Nuclear Physics for the verification of the helical mirror confinement idea. This concept involves active control of axial losses from the confinement zone in an open magnetic trap through the use of multiple mirrors that move in the plasma frame of reference. The discussed experiments focused on determining the cumulative effect of a helical mirror system in combination with a short segment of a stronger magnetic field. Combination of these two methods of axial flow suppression results in higher efficiency compared with each method individually. Different combinations of the mirrors were tested. The most effective flow suppression was observed if the short mirror was placed between the confinement region and the helical mirror. In this configuration, an effective mirror ratio of $R_{{\rm eff}} = 32.6\pm 7.8$ was achieved, along with a more than three-fold increase in plasma density within the confinement region. The possibility of a cumulative effect of different types of magnetic mirrors offers a way to improve the confinement performance of the reactor-grade mirror confinement devices.

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.

Development of a new magnetic mirror device at the Korea Advanced Institute of Science and Technology

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.

Toward continuum gyrokinetic study of high-field mirrors

High-temperature superconducting (HTS) magnetic mirrors under development exploit strong fields with high mirror ratio to compress loss cones and enhance confinement and may offer cheaper, more compact fusion power plant candidates. This new class of devices could exhibit largely unexplored interchange and gradient-driven modes. Such instabilities, and methods to stabilize them, can be studied with gyrokinetics, given the strong magnetization and prevalence of kinetic effects. Our focus here is to (a) determine if oft-used gyrokinetic models for open field lines produce the electron-confining (Pastukhov) electrostatic potential and (b) examine and address challenges faced by gyrokinetic codes in studying HTS mirrors. We show that a one-dimensional limit of said models self-consistently develops a potential qualitatively approaching the analytical Pastukhov level. Additionally, we describe the computational challenges of studying high mirror ratios with open field line gyrokinetic solvers and offer a force softening method to mitigate small time steps needed for time integration in colossal magnetic field gradients produced by HTS coils, providing a 19X speedup.

Temporal and Spatial Characteristics of Hard X-Ray Sources in a Flare Model with a Vertical Current Sheet

Abstract We analyzed changes in the height of the coronal hard X-ray (HXR) source for flares SOL2013-05-13T01:50 and SOL2013-05-13T15:51. Analysis of the Reuven Ramaty High Energy Solar Spectroscopic Imager data revealed the downward motion of the HXR source and the separation of the sources by energy and height. In the early stages of the flares, a negative correlation was found between the HXR source area in the corona and HXR flux. For the SOL2013-05-13T15:51 event, an increasing trend in the time delay spectra at the footpoints was obtained. For both events, the spectra of the time delays in the coronal HXR source showed a decreasing trend with energy in certain flare phases. To interpret the observed phenomena, we considered a flare model of collapsing traps and calculated the distribution functions of accelerated electrons along the magnetic loop using a nonstationary relativistic kinetic equation. This approach considers betatron and Fermi first-order acceleration mechanisms. The increasing trend of the time delay spectra at the footpoints was explained by the high mirror ratio in the magnetic loop and betatron acceleration mechanism. The observed features in the spatial and temporal behavior of the HXR sources, such as the negative correlation between the HXR source area and HXR flux, can be interpreted by the collapsing trap model.

Confinement time and ambipolar potential in a relativistic mirror-confined plasma

Advanced aneutronic fusion fuels such as proton-Boron11 tend to require much higher temperatures than conventional fuels like deuterium–tritium. For electrons, the bulk plasma temperature can approach a substantial fraction of the rest mass. In a mirror confinement system, where the electrons are confined by an ambipolar potential of at least five electron temperatures, the tail electrons which can escape the potential are fully relativistic, which must be taken into account in calculating their confinement. In this paper, simple estimates are employed to extend the scaling of the confinement time into the relativistic regime. By asymptotically matching this scaling to known solutions in the non-relativistic limit, accurate forms for the confinement time (and thus, the ambipolar potential) are obtained. These forms are verified using finite-element-based Fokker–Planck simulations over a wide range of parameters. Comparing relativistic and nonrelativistic mirror-confined plasmas with the same ratio of confining potential |eϕ| to electron temperature Te and the same mirror ratio R, the net result is a decrease in the confinement time due to relativistic effects by a factor of S≡(1+15Te/8mec2)/(1+2|eϕ|/mec2).

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.

Generation of multiply charged ions in accordance with geometry and magnetic field in Hall thruster plasmas

The production of multiply charged ions in Hall effect plasmas has been investigated. The factors that significantly affect plasma characteristics, such as geometry, magnetic field configuration, and magnetic mirror ratio, were analyzed. Among the co-current and counter-current configurations of a cylindrical Hall thruster (CHT) and an annular Hall thruster (AHT), the co-current configuration of the CHT shows the largest fractions of multiply charged ions. In particular, for the CHT, the region with high magnetic flux density had a significant influence on the fraction of multiply charged ions, but the fraction of multiply charged ions was not significantly different depending on magnetic mirror ratios. In addition, the configuration having a similar magnetic field in the CHT demonstrated comparable fractions of multiply charged ions and thrust even with different channel lengths. Hence, the broad region with the high magnetic flux density could enhance the probability of further ionization inside the discharge channel.

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.

Helical magnetic mirror performance at up- and downstream directions of the axial force

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 $R_{{\rm eff}}=3.3\pm 0.8$ ).

Controllability of Ion Out Flow Driven by Ambipolar Electric Field from Magnetic Mirror

A laminar flow is an ordered form of energy containers in plasma systems, hence tractable energy form to control or to convert to the other forms in plasmas. For this reason, plasma flows are utilized for various purposes, such as propulsion of spacecrafts, magnetohydrodynamic generators, and confinement of high-β fusion plasmas. In this study, we investigate properties of out flow of ions from a magnetic mirror in a laboratory experiment with a detailed measurement of axial profiles of plasma parameters for varied mirror ratios of the magnetic mirror. The experimental results reveal that the speed of the ion out flow is increased with the mirror ratio. This is considered to be attributed to enhancement of an ambipolar axial electric field accompanied by the increased mirror ratio. The relationship between the ambipolar potential height and the mirror ratio follows the relationship indicating a constant effective mirror ratio, which is an indication of an elimination of the mirror confinement effect by the enhanced ambipolar axial electric field. It is confirmed that the ion out flow satisfies the Bernoulli’s theorem and the continuity equation consistently. Accordingly, the ion out flow speed can be increased up to the speed corresponding to unity Mach number in the downstream of the magnetic mirror. Our work is the first detailed experimental confirmation of the Bernoulli’s theorem in a plasma flow system, which incorporates electrostatic potential variation in space. Another remarkable finding is that in the case of the mirror ratio lower than unity, the direction of the axial flow is reversed.

Fusion by beam ions in a low collisionality, high mirror ratio magnetic mirror

The classical problem of neutral beam ions slowing down in a magnetic mirror geometry is revisited to provide predictive capability for the new Wisconsin HTS Axisymmetric Mirror under development at the University of Wisconsin. A Fokker–Planck model named fast beam ion solver (FBIS) is developed to include the spatial non-uniformity of a physical mirror geometry. The mathematical framework allows for efficient orbit averaging of the pitch-angle scattering operator, and permits a determination of the axial profile of the ambipolar potential confining the electrons. The numerical results from FBIS are consistent with earlier work, but further show how mirror-ratio and a near square magnetic well optimizes the fusion gain. The numerical results are also applied to inform the conceptual design of WHAM++, a low capital-cost breakeven-class magnetic mirror device.

Finite orbit width effects in large aspect ratio stellarators

New orbit-averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity-space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS (Velasco et al., J. Comput. Phys., vol. 418, 2020, 109512; Velasco et al., Nucl. Fusion, vol. 61, 2021, 116013). The equations are used to study the $1/\nu$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/\nu$ regime transitions directly into the $\nu$ regime, without passing through a $\sqrt {\nu }$ regime. An explicit formula for the neoclassical fluxes in the $\nu$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrt {\nu }$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by Calvo et al. (Plasma Phys. Control. Fusion, vol. 59, 2017, 055014). In these stellarators, the $\sqrt {\nu }$ regime exists in the collisionality interval $(a/R) \ln (R/a) \ll \nu _{ii} R a/\rho _i v_{ti} \ll R/a$ . In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrt {\nu }$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $\delta$ : $\delta ^{2} |\ln \delta | \ll \nu _{ii} R a/\rho _i v_{ti} \ll 1$ . Here, $\nu _{ii}$ is the ion–ion collision frequency, $\rho _i$ and $v_{ti}$ are the ion gyroradius and thermal speed, and $a$ and $R$ are the minor and major radii.

Diverse Patterns and Clinical Significance of 11C-Methionine PET in Dysembryoplastic Neuroepithelial Tumors.

Dysembryoplastic neuroepithelial tumors (DNETs) are slow-growing epilepsy-associated tumors. Low or normal 11C-methionine (MET) PET uptake helps to differentiate DNETs from other low-grade gliomas. However, diverse MET-PET uptake in DNETs has been observed. The aim of this study is to measure the clinical significance and prognostic value of MET-PET in DNET management. Retrospective review of 26 DNET patients was done. Clinical characteristics, radiologic findings, and visual and quantitative MET-PET results were analyzed. PET uptake was calculated as the tumor-to-homotopic mirror ratio (TNRm) and tumor-to-contralateral cortex ratio (TNRc). The clinical activity of the tumors at the time of PET was classified into active and quiescent groups. The surgical outcome was defined as a composite of 2 different aspects: tumor progression and/or clinical events such as seizure recurrence or tumor bleeding. Twenty-seven MET-PET examinations (20 initial MET-PET and 7 MET-PET during follow-up) were included. Clinically active tumors at the time of PET presented significantly higher values of TNRm and TNRc than quiescent tumors. High MET-PET uptake by visual grading, TNRm ≥ 1.90, and TNRc ≥ 1.85 exhibited poor prognosis for event-free survival. MET-PET uptake correlates well with the clinical behavior of DNETs at the time of PET examination. Moreover, High MET-PET uptake is closely related to seizure recurrence if tumors are not entirely resected. Efforts to achieve gross total resection should be made for DNETs with high MET-PET uptake.

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.

Influence of magnetic configuration properties on kinetic ballooning modes in W7-X

The stability properties of kinetic ballooning modes are investigated for a number of magnetic configurations of the stellarator Wendelstein 7-X. In particular, we consider the effects of the vacuum rotational transform,${\raise.1pt-\kern-6pt\iota}$, and the mirror ratio. The analysis sheds light on the interplay between global magnetohydrodynamic configuration properties and local gyrokinetic stability, and is instrumental in the design of high-$\beta$(the ratio of kinetic to magnetic pressure) operation scenarios. In particular, it is demonstrated that some Wendelstein 7-X magnetic configurations have a relatively low kinetic ballooning mode threshold.

The 3D magnetic topology and plasma dynamics in open stochastic magnetic field lines

The thermal quench triggered by locked modes is known to be mainly due to open stochastic magnetic field lines connected to the wall boundary. It is essential to understand the 3D structure of open stochastic field lines since it determines the overall plasma dynamics in the system. In this study, we analyze the 3D magnetic topology for two key concepts, the connection length Lc and the effective magnetic mirror ratio Meff, and present a comprehensive picture of electron and ion dynamics related to the magnetic topology. The connection length determines the 3D structure of the ambipolar potential, and a sharp potential drop across distinct Lc regions induces the E × B transport and mixing across the field line. The confinement of electrons and ions along the field line is determined by the ambipolar potential and Meff configuration. Electron and ion temperatures in magnetic hills (Meff&amp;lt;1) are lower than in magnetic wells (Meff&amp;gt;1) because particles in magnetic hills are more likely to escape toward the wall boundary along the field line. The mixing between the magnetic wells and hills by E × B and magnetic drift motions results in collisionless detrapping of electrons and ions, which reduces their temperature efficiently. Numerical simulations of two different magnetic configurations demonstrate the importance of the collisionless detrapping mechanism, which could be the main cause of plasma temperature drop during the thermal quench.

Effects of Collision Velocity and Mirror Ratio on Collision/Merging Processes of Field-Reversed Configurations

Effects of Collision Velocity and Mirror Ratio on Collision/Merging Processes of Field-Reversed Configurations

Conceptual design of the ALIANCE-T mirror experiment

The paper describes the conceptual design of a small-scale experiment within the fusion neutron source project ALIANCE (Axisymmetric LInear Advanced Neutron sourCE). The experimental machine is an axially symmetric magnetic plasma trap with a high mirror ratio, which focuses on the physical and engineering problems of mirror-based gasdynamic neutron sources. The specific research topics covered include the magnetohydrodynamic (MHD) stability of plasmas with high mirror ratios, the operation of the electrodes used for plasma stabilization, and problems related to particle and energy transport. ALIANCE-T features superconducting mirror solenoids that enable it to reach mirror ratios of ∼100 and a helicon plasma source with a power of up to 25 kW installed directly in the confinement zone between the mirrors. The expected plasma parameters are estimated using a simple analytical model, which takes into account gasdynamic axial plasma losses, cross-field transport, and the interaction of the plasma with neutral gas. It is projected that the machine will simultaneously achieve a plasma density >1013 cm−3 and a temperature >10 eV in a continuous discharge lasting for 1–8 h. This paper gives a detailed description of the key machine subsystems and introduces the analytical model used for calculation of the plasma parameters.

Development of ECR ion source with high-temperature superconducting REBCO coils

A new High-Temperature Superconducting ECR (HTS-ECR) ion source is under development in Research Center for Nuclear Physics (RCNP), Osaka University. This ion source will be used for production of high intensity proton, deuteron and He ion beams. The HTS-ECR magnets are composed of three solenoid coils and a set of sextupole coils made of REBCO tapes, a high-temperature superconductor. The HTS-ECR ion source is designed to operate at frequency of 2.45 GHz and 10 GHz. Performance test of the HTS coils had been carried out at 31 K and 77 K. This HTS coil technology will be applied to development of a meter-size HTS coil system of a high intensity compact AVF cyclotron. This paper introduces the basic design of the HTS-ECR ion source. The performance test results showed that REBCO solenoids remain superconducting state with a current up to 400 A. Simulation results of the magnetic field and electromagnetic field distributions in a plasma chamber fulfilled the requirements of electron cyclotron resonance conditions at 2.45 GHz and 10 GHz. Simulation result of mirror ratios and electromagnetic field amplitudes are also presented in this paper.