Mirror Ratio Research Articles

Plasma flow suppression by the linear helical mirror system

The paper presents experimental results from the SMOLA device that is the first facility with a helical mirror section of the magnetic system. This device was built in the Budker Institute of Nuclear Physics for the verification of the helical mirror confinement idea that is the technique of an 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 the increase in plasma density in the entrance trap by a factor of 1.6 in the helical configuration. The integral axial flux from the transport section drops severalfold. The effective mirror ratio of the helical section was $R_{eff} > 10$ . Particle flux returning by the helical mirror section towards the confinement zone was observed. At high corrugation ratios, the axial flux direction is different at the magnetic axis and in the periphery of the plasma in the helical section. All axial fluxes scale linearly with the plasma density, even if the ion mean free path is comparable to the total length of the helical section. Good agreement of the experimental results with theoretical predictions is found.

Influence of axial mirror ratios on the kinetic instability threshold in electron cyclotron resonance ion source plasma

Electron Cyclotron Resonance (ECR) ion source plasmas are prone to kinetic instabilities. The onset of the instabilities manifests as emission of microwaves, bursts of electrons expelled from the plasma volume, and the collapse of the extracted highly charged ion (HCI) currents. Consequently, the instabilities limit the HCI performance of ECR ion sources by limiting the parameter space available for ion source optimization. Previous studies have shown that the transition from stable to unstable plasma regime is strongly influenced by the magnetic field structure, especially the minimum field value inside the magnetic trap (Bmin). This work focuses to study the role of the magnetic confinement on the onset of the kinetic instabilities by probing the influence of the injection and extraction mirror field variation on the instability threshold. The experiments have been performed with a room-temperature 14.5 GHz ECR ion source with an axially movable middle coil that provides flexible control over the axial field profile and especially the Bmin, which was used to quantify the variation in the instability threshold. The experimental results show that variation of the extraction field Bext, which defines the weakest magnetic mirror, correlates systematically with the variation of the instability threshold; decreasing the Bext allows higher threshold Bmin. The result demonstrates the importance of electron confinement and losses on the plasma stability. The connection between the weakest mirror field and the onset of instabilities is discussed taking into account the variation of magnetic field gradient and resonance plasma volume.

Transport of fast electron beam in mirror-field magnetized solid-density plasma

In experiments on the effect of magnetic field on electron transportation in laser–plasma interaction, the magnetic field is often produced by two coils and is mirror-like. In this paper, the transport and the reflection of fast electron beam generated in laser–plasma interaction in solid-density plasma immersed in a mirror magnetic field are studied using particle-in-cell simulation. The helicoidal motion of fast electrons in the field and the convergence of magnetic induction lines leads to the collimated transport and focusing of the fast electrons. The reflection of the fast electrons can lead to the decrease in the transmission ratio, and this reflection increases with the magnetic mirror ratio, but saturates at a certain level.

Numerical analysis of heat load distribution in Heliotron J with magnetic field tracing and plasma transport modeling

We model and characterize the heat load patterns on the vacuum chamber wall in an advanced helical device, Heliotron J, based on the peripheral transport code EMC3-EIRENE, in three typical magnetic configurations with different toroidal mirror ratios (bumpiness). The heat flux distribution on the vacuum chamber wall evaluated with the EMC3-EIRENE code shows several groups of heat flux footprints, some of which are not seen in the connection length distribution obtained with the magnetic field tracing code. This clearly shows the necessity for plasma modeling in addition to magnetic field line tracing in the design of three-dimensional devices. At high electron density, a displacement and an expansion of the heat flux distribution in both the toroidal and poloidal directions are observed. As a result of the heat flux expansion, the peak value of the heat flux decreases at high electron density. Further, an approach that uses the heat distribution function is proposed to evaluate the global power distribution in the entire vacuum chamber. The evaluation results confirm a decrease in the peak heat flux and an increase in the plasma-wetted area at high electron density. The heat flux distribution expansion is larger for the low-bumpiness configuration, in which the peak heat value is by more than lower than that for the high-bumpiness configuration.

Confinement of relativistic electrons in a magnetic mirror en route to a magnetized relativistic pair plasma

Creating a magnetized relativistic pair plasma in the laboratory would enable the exploration of unique plasma physics relevant to some of the most energetic events in the universe. As a step toward a laboratory pair plasma, we have demonstrated an effective confinement of multi-MeV electrons inside a pulsed-power-driven 13 T magnetic mirror field with a mirror ratio of 2.6. The confinement is diagnosed by measuring the axial and radial losses with magnetic spectrometers. The loss spectra are consistent with ≤2.5 MeV electrons confined in the mirror for ∼1 ns. With a source of 1012 electron-positron pairs at comparable energies, this magnetic mirror would confine a relativistic pair plasma with Lorentz factor γ∼6 and magnetization σ∼40.

A 24.4 ppm/°C Voltage Mode Bandgap Reference With a 1.05V Supply

This brief proposes a sub-1V, voltage mode CMOS bandgap reference circuit. Conventionally, sub-1V references are obtained by converting PTAT and CTAT voltages to currents and summing them in the current domain. Such techniques have multiple operating points and cannot natively support applications that require PTAT currents in addition to a bandgap voltage. This brief presents a voltage mode reference circuit, which adds a PTAT voltage with a scaled version of a CTAT voltage all within the sub-1V domain. Compared to current mode bandgaps, summing in voltage domain enables reduction of one CTAT current mirror stage and a significant reduction in PTAT current mirror ratio resulting in a reduced number of error sources. In addition, this circuit also natively supports applications that require PTAT current. A novel, high-accuracy self-biasing technique has been adopted to minimize the systematic offset induced temperature coefficient. A prototype designed in 45nm TSMC CMOS technology for a nominal voltage of 500mV demonstrates 24.4ppm/°C temperature coefficient from -40°C to 125°C, 0.15% line regulation, and draws 7.2μ\textA from a 1.05V supply.

Preliminary experimental scaling of the helical mirror confinement effectiveness

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.

Helicon plasma in a magnetic shuttle

The definition of a magnetic shuttle is introduced to describe the magnetic space enclosed by two magnetic mirrors with the same field direction and high mirror ratio. Helicon plasma immersed in such a magnetic shuttle (mirror ratio 5) that can provide the confinement of charged particles is modeled using an electromagnetic solver. The perpendicular structure of the wave field along this shuttle is given in terms of stream vector plots, showing a significant change from midplane to ending throats, and the vector field rotates and forms a circular layer that separates the plasma column radially into core and edge regions near the throats. The influences of the driving frequency (f = 6.78 MHz–40.68 MHz), plasma density (nemax = 1016 m−3 to 1019 m−3), and field strength (B0max = 0.017 T–1.7 T) on the wave field structure and power absorption are computed in detail. It is found that the wave energy and power absorption decrease for increased driving frequency and reduced field strength and increase significantly when the plasma density is above a certain value. The axial standing-wave feature always exists, due to the interference between forward and reflected waves from ending magnetic mirrors. Distributions of wave energy density and power absorption density all show a shrinking feature from midplane to ending throats, which is consistent with the nature of the helicon mode that propagates along field lines. Theoretical analysis based on a simple magnetic shuttle and the governing equation of helicon waves shows consistency with computed results and previous studies. This hypothetical work is a valuable to guide the helicon physics prototype experiment, which is designed for the fundamental wave–particle interaction study in helicon plasma, to achieve high plasma density and energy absorption efficiency.

Magnetic shaping for a minimum B trap

• A minimum B field provides MHD stability, but a threat is the flux tube ellipticity, which is optimized in the study. • The magnetic shaping minimizes the flux tube ellipticity and neoclassical effects with MHD stability preserved. · • A controlled weak radial electric field restricts the guiding center motion to the immediate vicinity of a flux surface. · • Superconducting 3D coils have been computed which reproduce the derived magnetic field. · • In a minimum B vacuum field, a finite plasma beta may increase the mirror ratio to values exceeding 10. A mirror machine with a minimum B field for MHD stability is an option for a steady-state compact fusion neutron source design. A previous calculation of an idealized quadrupolar mirror field in Ref Ågren and Moiseenko (2017) is extended to a magnetic field which smoothly evolves to expander regions beyond the mirror throats. In a minimum B field, the projection of a flux surface on planes perpendicular to the magnetic axis evolves from a circular shape at the mid-plane to a highly elliptical shape as the mirror ratio is increased. Magnetic shaping is made to find the minimal ellipticity. The ellipticity depends sensitively on the gyro center magnetic drift in the confinement region, and the optimal result approaches a state where the magnetic drift is made as small as possible, which corresponds to the SFLM (Straight Field Line Mirror) field. In such a magnetic field, in combination with a weak radial electric field, each guiding center is forced to move close to its mean magnetic surface, thereby suppressing neoclassical transport effects. Biased end plates, placed at the end tank outside the confinement region, is a tool to control the radial electric field. The biased end plates could also assist to more precisely determine the positioning of drift surfaces in the confinement region. The reproduction of the optimized magnetic field with superconducting coils is a challenge due to the strong gradients in B . This is solved by a special arrangement with compact 3D superconducting coils, and the reproduction of the magnetic field is demonstrated with a mirror ratio of 4. Mirror ratios exceeding 10 may be reachable with finite β effects included. Analytical expressions in closed form are derived.

Effects of magnetic configuration on hot electrons in a minimum-B ECR plasma

To investigate the hot electron population and the appearance of kinetic instabilities in highly charged electron cyclotron resonance ion source (ECRIS), the axially emitted bremsstrahlung spectra and microwave bursts emitted from ECRIS plasma were synchronously measured on SECRAL-II (Superconducting ECR ion source with Advanced design in Lanzhou No. II) ion source with various magnetic field configurations. The experimental results show that when the ratio of the minimum field to the resonance field (i.e. Bmin/Becr) is less than ∼0.8, the bremsstrahlung spectral temperature Ts increases linearly with the Bmin/Becr–ratio when the injection, extraction and radial mirror fields are kept constant. Above this threshold Ts saturates and the electron cyclotron instability appears simultaneously. This study has also demonstrated that Ts decreases linearly with the increase of the average gradient over the ECR surface when the on-axis gradient and hexapole field strengths are constant. In addition, it is found that Ts decreases with the increase of the gradient at the resonance zone (∇Becr on axis and <∇Becr>) at relatively low mirror ratio and is insensitive to the gradient at high mirror ratio when Bmin is constant. Compared to a recent study taken on a fully superconducting ECRIS (Benitez et al 2017 IEEE Trans. Plasma Sci. 45 1746–54), in which it was concluded that Ts is only sensitive with Bmin, this article shows different results discussing the mechanisms behind the correlation of magnetic field parameters to Ts.

Improvement of Electron Recovery Using a Magnetic Field with a Low Mirror Ratio in a Secondary Electron Direct Energy Converter Simulator

Improvement of Electron Recovery Using a Magnetic Field with a Low Mirror Ratio in a Secondary Electron Direct Energy Converter Simulator

Intensification of laser-produced relativistic electron beam using converging magnetic fields for ignition in fast ignition laser fusion

The kilo-tesla-class converging magnetic field effects on the core heating properties and the energy and duration of relativistic electron beam (REB) required for ignition in fast ignition laser fusion has been evaluated by parametric 2D hybrid simulations where a uniformly compressed DT core with ρ = 300 g/cm3 is heated by REB with TREB = 3 MeV, IREB = 0.69 × 1020 W/cm2 and θREB = 40° under sufficiently strong magnetic field (Bext = 3 kT at the REB injection position). The kilo-tesla-class converging magnetic field can intensify REB and then enhances the core heating power drastically. As the results, the fusion ignition can be initiated by the REB with EREB ≧ 50 kJ and τREB = 10 ~ 30 ps. With increasing mirror ratio RM, the negative effect of converging field, i.e., mirror reflection, becomes significant, which enhances the REB energy required for ignition (EREB,ig = 49 kJ for RM = 3 → EREB,ig =77 kJ for RM = 20).

Study on the influence of magnetic mirror ratio on the erosion of the bottom channel of cylindrical Hall thruster with magnetically insulated anode

A cylindrical Hall thruster with a magnetically insulated anode structure was found experimentally to experience erosion sputtering at the bottom of the ceramic channel. In this study, a Particle-In-Cell numerical simulation was used to analyze the influence of the magnetic mirror effect on the ion current density, ion energy, and deposition power density bombardment at the bottom of the discharge channel. The research findings show that, as the magnetic mirror ratio grows, the stronger magnetic mirror effect confines the ions in the boron nitride channel, leading to a decrease in the ion current density and ion energy bombarding the bottom of discharge bottom. Further statistics show that the deposition power density decreases as the magnetic mirror ratio grows, indicating that increasing the magnetic mirror ratio can effectively alleviate the erosion sputtering at the bottom.

Experimental Investigation of the Effects of Magnetic Mirrors on Plasma Transport in the Prototype Material Plasma Exposure Experiment

The Prototype Material Plasma Exposure eXperiment (Proto-MPEX) at Oak Ridge National Laboratory is developing a helicon radio frequency (RF) source for plasma production along with microwave electron heating and RF ion heating. Proto-MPEX has several magnetic mirrors that affect plasma transport. The magnetic field near the helicon source is ~ 0.05 T, and the peak magnetic field in Proto-MPEX is ~ 1.8 T, which results in a large magnetic well for particles sourced at the helicon transporting toward the target region. Keeping the helicon source field and the target field constant, experiments have been conducted by methodically changing the magnetic field, at a local axial location, within the source and the target. Plasma flow measurements using Mach probes have shown a decrease in the flow as a function of the magnetic mirror ratio. Plasma flows were further investigated with ion cyclotron resonant heating (ICH). Results with the addition of ICH measured upstream of the antenna have shown a decrease in Mach number as a function of mirror ratio when compared to helicon discharges. Such flow behavior demonstrated slowing down of the plasma due to the increased reverse plasma flow toward the helicon plasma source. However, in high magnetic fields, when the resonant magnetic field moved away from the ICH antenna, no effects on the plasma flow due to ICH were observed.

Confinement of proton beam in a magnetic mirror

By using particle-in-cell(PIC) simulation method, the proton beam confinement in a magnetic mirror is investigated in the present paper. We define two physical quantities to describe the confinement effects of mirror for proton beam. One is loss rate χ=Nlost/N0, where Nlost is the number of leaked particles from the mirror and N0 is the number of initial particles. The other is confinement time τm. Dependences of loss rate and confinement time on the parameters of both magnetic mirror and proton beam is given. It is found that the larger the mirror ratio, the less the loss rate, and the longer the confinement time. The appropriate proton beam velocity and other parameters of the protons can significantly improve the confinement time of the mirror and the efficiency of confinement.

Electrostatic equilibria of non-neutral plasmas confined in a Penning trap with axially varying magnetic field

A procedure for computing the electrostatic equilibria of non-neutral plasmas in a Penning trap with a nonuniform magnetic field by solving Poisson's equation using an iterative method is described. Plasma equilibria in a model Penning trap with high and low field regions are computed. The plasma is assumed to follow the Boltzmann density distribution along magnetic field lines. Correspondence with previous investigations examining similar configurations analytically and using particle-in-cell simulations is found. The relationship between the plasma density in low and high field regions is examined for various plasma temperatures, densities, magnetic mirror ratios, and plasma and electrode radii. An analytical description of the radial density profile in the high field region is developed and compared with the computed equilibria. A concept is described for cooling a positron plasma with laser-cooled ions trapped axially within a high magnetic field region, while antiprotons are trapped axially separated from the laser-cooled ions within a low field region, and the positron plasma extends to both regions.

Design and calibration of a retarding field energy analyzer for the LTX-β scrape off layer and modeling of electrostatic potential in a collisionless SOL

Abstract The Lithium Tokamak eXperiment (LTX) is a spherical tokamak device designed to study lithium plasma facing components (PFCs). The lithium coated wall of LTX has been demonstrated to produce a plasma edge with high electron temperature (200 eV or greater). Plasma density in the outer scrape-off layer (SOL) is also found to be very low, around 2 × 1017m-3, as a result of the low recycling lithium boundary. The high temperature, low collisionality region of the plasma extends into the SOL. The recent upgrade to LTX-β includes installation of a neutral beam, which will provide further heating and fueling of the core plasma. Core and edge diagnostics will also be expanded. As part of this expansion, a Retarding Field Energy Analyzer (RFEA) has been developed for the SOL of LTX-β. Measurements of the ion temperature, ion energy distribution, and the local space potential will be performed in the SOL plasma using this RFEA. Upgraded high field side (HFS) and low field side (LFS) Langmuir probes will replace existing triple probes so that higher electron temperatures can be more reliably measured. The HFS probes are also positioned to give radial and vertical gradient measurements. The design of the RFEA will be presented, along with calibration data. Since a high temperature, low collisional edge is expected for LTX-β, with a high mirror ratio near the LCFS (around 4), the majority of particles in the SOL will be mirror-trapped. Trapped particle effects will therefore become significant in the physics of the SOL plasma, and warrant further theoretical investigations. Here we present a theoretical study of the ambipolar potential formed in the collisionless SOL via differential loss of the electrons and ions, known as the Pastukhov potential in the literature. Numerical results will also be presented.

Effect of anode magnetic shield on inner magnetic pole etched in anode layer Hall thruster

For anode layer Hall plasma thruster, the etching of inner magnetic pole is one of the key factors affecting its service life. In order to solve the problem of inner magnetic pole etching in anode layer Hall plasma thruster, the effect of anode magnetic shield on inner magnetic pole etched in anode layer Hall thruster is studied by combining particle simulation PIC with sputtering simulation. The magnetic shielding of anode changes the distribution of magnetic field configuration on the surface of the anode, and improves the magnetic mirror ratio of the magnetic mirror field of the thruster to the magnetic field width of the positive gradient on the central axis. The ratio of the magnetic mirror is 1.4 times that of the original one, and two additional saddle magnetic fields are added on both sides of the original saddle magnetic field region. It not only is conducive to confining electrons and improving the ionization rate of working gas, but also keeps a certain distance between the anode and the high temperature electron region, which provides the reliable reference data for the design of high power Hall plasma thruster. When the discharge voltage is 900 V and the working pressure is 2 × 10&lt;sup&gt;–2&lt;/sup&gt; Pa, the simulation results show that after the anode is shielded by the magnetic shield, the energy range of most of the incident ions on the inner magnetic pole is 40–260 eV, which is 100 eV lower than the energy range 40–360 eV in the case without shielding the anode. The probability distribution of particle energy without magnetically shielding the anode between 260 eV and 600 eV is obviously higher than that of ion energy with magnetically shielding the anode. The maximum probability distribution of cosine value of incident angle is extended from a small range near 0.1 (incident angle 84°) to a large range of 0.1–0.45 (incident angle 84°–63°). The magnetic shielding makes the incident ions disperse on the surface of the inner magnetic pole, which is helpful in reducing the etching of inner magnetic pole. The maximum etching rate of inner magnetic pole after the anode has been magnetically shielded is reduced from 16 × 10&lt;sup&gt;–10&lt;/sup&gt; m/s to 6.1 × 10&lt;sup&gt;–10&lt;/sup&gt; m/s, which is 2.62 times lower. The comparison of simulation results with experimental results in the case without magnetically shielding the anode shows that they are in good agreement.

Study of the influence of magnetic field profile on plasma parameters in a simple mirror trap

This work presents the multiple diagnostics characterization of the plasma in an axis-symmetric simple mirror trap as a function of magnetic field profile (mirror ratios and magnetic field gradient), especially in the quasi-flat B field configuration that is typical of Microwave Discharge Ion Sources, and also of neutral gas pressure and microwave power. The simultaneous use of Optical Emission Spectroscopy, Langmuir Probe and X-ray diagnostics allows the characterization of the whole electron energy distribution function (EEDF), from a few eV to hundreds of keV . Results show non-linear behaviour under small variations of even one source parameter and strong influence on EEDF of the Bmin/BECR ratio. Benefit and next developments will be highlighted.

Effect of magnetic shear on edge turbulence in SOL-like open field line configuration in QUEST

Intensity fluctuations are investigated using the fast camera imaging technique in the slab annular plasma as a function of magnetic shear and connection length in the spherical tokamak QUEST. Note that here QUEST is operated as a simple magnetized torus with a tight aspect ratio. Slab annular plasmas feature open magnetic field lines and can mimic the tokamak edge-scrape off layer (SOL)-like plasma attributes reasonably well. Three magnetic shear regimes are realized using three poloidal magnetic field (PF) coil pairs. A whole range of connection lengths (∼∞ ≥ Lc ≥ 5.5 m) is scanned by varying the PF strength for a given toroidal field for each magnetic shear regime. For the first time a systematic study of the effect of magnetic shear and field line pitch together on edge-SOL-like plasma fluctuations is being reported. Slab plasmas with intermediate magnetic shear are observed to be more susceptible to generate distinct blobs when Lc is reduced by increasing the PF strength. A distinct coherent mode appears only at the lowest magnetic shear slab featuring a deep potential well. Such mode is not apparent at other magnetic shear cases even at the same Lc. Finally, with a combination of PF coil pairs, both the features of intermediate and low magnetic shear slabs are shown to be realizable simultaneously. Significantly stronger blobs are observed with such combination of PF mirror ratios in the presence of a coherent mode. This study may provide better insight into the effect of magnetic configuration in the tokamak edge and SOL turbulence and can help in searching for better tools to control cross-field convective intermittent transport in tokamaks.