Inductive Helicity Injection Research Articles

Effects of temperature and density evolution in MHD simulations of HIT-SI

The helicity injected torus-steady inductive (HIT-SI) experiment uses steady inductive helicity injection to form a spheromak equilibrium and sustain the structure against resistive decay. Helicity injection is performed using two half-tori “injectors” connected to the main plasma volume, whose fields are oscillated in an AC manner. The properties of the sustained spheromak equilibrium have been experimentally observed to vary with the frequency of the injector oscillation, producing higher current gains and more-symmetric and outwardly shifted current centroids with higher frequency. A computational scan of injector frequency using the 3D MHD code PSI-Tet, which models the entire HIT-SI plasma volume including the injectors, has been performed, including a comparison of the results using the full Hall MHD model to those obtained using a simplified “zero-beta” (constant temperature and density) model. The results of both PSI-Tet models are also compared with experimental data and with simulations using the NIMROD code, which does not model the injector regions. The results of the PSI-Tet simulations show that the average temperature and current gain increase with injector frequency, in agreement with experimental trends. The simulations also show qualitative changes in the dynamics of several quantities with increasing injector frequency, such as density oscillations and current evolution. However, the outward shift and symmetrizing of the current centroid, observed experimentally, are not observed in these MHD simulations, indicating that unresolved or excluded dynamics may be important.

Formation of closed flux surfaces in spheromaks sustained by steady inductive helicity injection

The helicity injected torus with steady inductive helicity injection device is a simply-connected toroidal device that forms and sustains axisymmetric spheromak equilibria through the use of steady inductive helicity injection, which inject magnetic helicity through the inductive drive of non-axisymmetric currents on the edge of the plasma. Simulations of high-gain scenarios, using the NIMROD code and based on models validated with low gain experimental operations, indicate the formation of closed flux surfaces at current amplifications of six. Despite the helicity injection scheme adding magnetic perturbations of order , these closed flux equilibria are able to persist for as long as 20 injector periods (1.3 ms) before breaking apart due to other plasma generated instabilities.

Derivation of dynamo current drive in a closed-current volume and stable current sustainment in the HIT-SI experiment

A derivation is given showing that the current inside a closed-current volume can be sustained against resistive dissipation by appropriately phased magnetic perturbations. Imposed-dynamo current drive theory is used to predict the toroidal current evolution in the helicity injected torus with steady inductive helicity injection (HIT-SI) experiment as a function of magnetic fluctuations at the edge. Analysis of magnetic fields from a HIT-SI discharge shows that the injector-imposed fluctuations are sufficient to sustain the measured toroidal current without instabilities whereas the small, plasma-generated magnetic fluctuations are not sufficiently large to sustain the current.

Numerical studies and metric development for validation of magnetohydrodynamic models on the HIT-SI experimenta)

We present application of three scalar metrics derived from the Biorthogonal Decomposition (BD) technique to evaluate the level of agreement between macroscopic plasma dynamics in different data sets. BD decomposes large data sets, as produced by distributed diagnostic arrays, into principal mode structures without assumptions on spatial or temporal structure. These metrics have been applied to validation of the Hall-MHD model using experimental data from the Helicity Injected Torus with Steady Inductive helicity injection experiment. Each metric provides a measure of correlation between mode structures extracted from experimental data and simulations for an array of 192 surface-mounted magnetic probes. Numerical validation studies have been performed using the NIMROD code, where the injectors are modeled as boundary conditions on the flux conserver, and the PSI-TET code, where the entire plasma volume is treated. Initial results from a comprehensive validation study of high performance operation with different injector frequencies are presented, illustrating application of the BD method. Using a simplified (constant, uniform density and temperature) Hall-MHD model, simulation results agree with experimental observation for two of the three defined metrics when the injectors are driven with a frequency of 14.5 kHz.

Simulation of injector dynamics during steady inductive helicity injection current drive in the HIT-SI experiment

We present simulations of inductive helicity injection in the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI) device that treats the entire plasma volume in a single dynamic MHD model. A new fully 3D numerical tool, the PSI-center TETrahedral mesh code, was developed that provides the geometric flexibility required for this investigation. Implementation of a zero-β Hall MHD model using PSI-TET will be presented including formulation of a new self-consistent magnetic boundary condition for the wall of the HIT-SI device. Results from simulations of HIT-SI are presented focusing on injector dynamics that are investigated numerically for the first time. Asymmetries in the plasma loading between the two helicity injectors and progression of field reversal in each injector are observed. Analysis indicates cross-coupling between injectors through confinement volume structures. Injector impedance is found to scale with toroidal current at fixed density, consistent with experimental observation. Comparison to experimental data with an injector drive frequency of 14.5 kHz shows good agreement with magnetic diagnostics. Global mode structures from Bi-Orthogonal decomposition agree well with experimental data for the first four modes.

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code

We present a comparison study of 3-D pressureless resistive MHD (rMHD) and 3-D presureless two-fluid MHD models of the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI). HIT-SI is a current drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The comparable size of the collisionless ion skin depth di to the resistive skin depth predicates the importance of the Hall term for HIT-SI. The simulations are run with NIMROD, an initial-value, 3-D extended MHD code. The modeled plasma density and temperature are assumed uniform and constant. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification ItorIinj and formation time τf demonstrated by HIT-SI with similar internal magnetic fields. rMHD underestimates ItorIinj and exhibits much a longer τf. Biorthogonal decomposition (BD), a powerful mathematical tool for reducing large data sets, is employed to quantify how well the simulations reproduce the measured surface magnetic fields without resorting to a probe-by-probe comparison. BD shows that 2fl-MHD captures the dominant surface magnetic structures and the temporal behavior of these features better than rMHD.

Relaxation-time measurement via a time-dependent helicity balance model

A time-dependent helicity balance model applied to a spheromak helicity-injection experiment enables the measurement of the relaxation time during the sustainment phase of the spheromak. The experiment, the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI), studies spheromak formation and sustainment through inductive helicity injection. The model captures the dominant plasma behavior seen during helicity injection in HIT-SI by using an empirical helicity-decay rate, a time-dependent helicity-injection rate, and a composite Taylor state to model both the helicity content of the system and to calculate the resulting spheromak current. During single-injector operations, both the amplitude and the phase of the periodic rise and fall of the toroidal current are predicted by this model, with an exchange of helicity between the injector states and the spheromak state proposed as the causal mechanism. This phenomenon allows for the comparison of the delay between the current rises in the experiment and the numerical model, enabling a measurement of the relaxation time. The measured relaxation time of 4.8 μs ± 2.8 μs is shorter than the toroidal Alfvén timescale. These results validate Hall MHD calculations of the Geospace Environmental Modeling challenge.

Imposed-dynamo current drive

A mechanism for steady inductive helicity injection (SIHI) current drive has been discovered where the current driving fluctuations are not generated by the plasma but rather are imposed by the injectors. Sheared flow of the electron fluid distorts the imposed fluctuations to drive current. The model accurately predicts the time dependent toroidal current, the injector impedance scaling, and the profile produced in the HIT-SI experiment. These results show that a stable equilibrium can be efficiently sustained with imposed fluctuations and the current profile can, in principle, be controlled. Both are large steps for controlled fusion. Some of the effects of the fluctuations on the confinement of tokamak and spheromak reactors are assessed and the degradation may be tolerable. The mechanism is also of interest to plasma self-organization, fast reconnection and plasma physics in general.

Advances in Steady Inductive Helicity Injection for Plasma Startup and Toroidal Current Drive

The Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) has achieved a breakthrough in the development of a new method of toroidal plasma startup and current drive. HIT-SI accomplishes helicity injection current drive on a spheromak of major radius 0.3 m with two injectors driven sinusoidally at 14.5 kHz. Results include the first sustainment of toroidal plasma current of over 50 kA at up to 3 times the injected currents added in quadrature. Separatrix toroidal currents—currents not linking the helicity injectors—are sustained at up to 40 kA. Toroidal currents persist for up to 0.65 ms after the injectors are turned off. Results are achieved after helium operations condition the alumina plasma-facing surface. The conditioned alumina walls then act to pump the deuterium, thereby reducing the spheromak density. High performance discharges (Itor/Iinj ≥ 2) are characterized by a decrease in the n = 1 mode activity measured by surface probes near the midplane of the confinement volume. Suppression of internal magnetic fields (measured by an internal probe) below the predicted Taylor equilibrium indicates that the magnetic fields in HIT-SI can no longer be described by a zero pressure, constant λ equilibrium.

Evidence for Separatrix Formation and Sustainment with Steady Inductive Helicity Injection

The first sustainment of toroidal plasma current of 50 kA at up to 3 times the injected currents, added in quadrature, using steady inductive helicity injection is described. Separatrix currents-currents not linking the helicity injectors-are sustained up to 40 kA. Decreases in the n=1 toroidal mode of the poloidal magnetic field at higher current amplifications indicate more quiescent, direct toroidal current drive. Results are achieved in HIT-SI (with a spheromak of major radius 0.3 m) during deuterium operations immediately after helium operation. These results represent a breakthrough in the development of this new current drive method for magnetic confinement fusion.

Recent results from the HIT-SI experiment

New understanding and improved parameters have been achieved on the Helicity Injected Torus with Steady Inductive helicity injection current drive (HIT-SI) experiment. The experiment has a bowtie-shaped spheromak confinement region with two helicity injectors. The inductive injectors are 180° segments of a small, oval cross section toroidal pinch. Spheromaks with currents up to 38 kA and current amplification of 2 have been achieved with only 6 MW of injector power. The Taylor-state model is shown to agree with HIT-SI surface and internal magnetic profile measurements. Helicity balance predicts the peak magnitude of toroidal spheromak current and the threshold for spheromak formation. The model also accurately predicts the division of the applied loop voltage between the injector and spheromak regions. Single injector operation shows that the two injectors have opposing, preferred spheromak current directions. An electron locking relaxation model is consistent with the preferred direction, with ion Doppler data and with bolometric data. Results from higher frequency operation are given. The impact of the new understanding on the future direction of the HIT programme is discussed.

Internal Fields in Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) Discharges

The Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) consists of an axisymmetric flux conserver and two half-torus magnetic helicity injectors, mounted on either side of the axisymmetric confinement region (Jarboe et al., 2006, Phys. Rev. Lett., 97, 115003). Current and flux are driven sinusoidally with time in each injector, injecting both power and magnetic helicity into the HIT-SI device, with the goal of forming and sustaining a spheromak in the confinement region. Recent HIT-SI results include formation of discharges with toroidal spheromak current 1.5 times the injector current amplitude, development of a Taylor-state model for the magnetic fields in HIT-SI discharges, and direct measurement of the portion of the induced injector electric field that drives current in the confinement region.

Overview of the Helicity Injected Torus (HIT) Program

The Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) consists of a "bowtie"-shaped axisymmetric confinement region, with two half-torus helicity injectors mounted on each side of the axisymmetric flux conserver [Sieck et al, IEEE Trans. Plasma Sci., v.33, p.723 (2005); Jarboe, Fusion Technology, v.36, p.85 (1999)]. Current and flux are driven sinusoidally with time in each injector, with the goal of generating and sustaining an axisymmetric spheromak in the main confinement region. Improvements in machine conditioning have enabled systematic study of HIT-SI discharges with significant toroidal current I TOR , including cases in which this current I TOR switches sign one or more times during the discharge. Statistical studies of all HIT-SI discharges to date demonstrate a minimum injected power to form significant I TOR , and that the maximum I TOR scales approximately linearly with the total injected power.

Spheromak Formation by Steady Inductive Helicity Injection

A spheromak is formed for the first time using a new steady state inductive helicity injection method. Using two inductive injectors with odd symmetry and oscillating at 5.8 kHz, a steady state spheromak with even symmetry is formed and sustained through nonlinear relaxation. A spheromak with about 13 kA of toroidal current is formed and sustained using about 3 MW of power. This is a much lower power threshold for spheromak production than required for electrode-based helicity injection. Internal magnetic probe data, including oscillations driven by the injectors, agree with the plasma being in the Taylor state. The agreement is remarkable considering the only fitting parameter is the amplitude of the spheromak component of the state.

Demonstration of steady inductive helicity injection

Initial results demonstrating the concept of constant inductive helicity injection are presented. Constant helicity injection is achieved using two oscillating inductive helicity injectors, with the goal of producing a bow tie spheromak. Each injector is a 180° segment of a reverse field pinch and they are driven 90° out of phase. Approximately 5 MW of power is injected during the 6 ms pulse, and the input power has been maintained at a fairly constant value by directly fuelling the injectors with neutral gas. Motivation for the experiment is given, including beta-limit calculations for the bow tie spheromak. Fuelling the injectors with neutral gas during the discharge is shown to produce injector parameters that are more constant in time. A series of discharges with increasing power input shows a promising increase in toroidal current. Unique construction techniques of the experiment are also described.

Three-dimensional magnetohydrodynamic simulations of the Helicity Injected Torus with Steady Inductive drive

The Helicity Injected Torus with Steady Inductive drive (HIT-SI) [P. E. Sieck, W. T. Hamp, V. A. Izzo, T. R. Jarboe, B. A. Nelson, R. G. O’Neill, A. J. Redd, and R. J. Smith, IEEE Conference Record—Abstracts. 31st IEEE International Conference On Plasma Science (IEEE Catalog No. 04CH37537), 2004, p. 160] is a spheromak driven by steady inductive helicity injection (SIHI) and consists of the toroidally symmetric spheromak confinement region and two nonsymmetric helicity injectors. The three-dimensional (3D) magnetohydrodynamic code NIMROD [A. H. Glasser, C. R. Sovinec, R. A. Nebel, T. A. Gianakon, S. J. Plimpton, M. S. Chu, and D. D. Schnack, Plasma Phys. Controlled Fusion, 41, A747 (1999)] is used to simulate HIT-SI operation, but the code’s toroidally symmetric boundary requires a creative treatment of the injectors. Sustained HIT-SI operation is simulated with nonaxisymmetric boundary conditions. In driven simulations at low Lundquist number S no n=0 fields are generated as a result of relaxation of the predominantly n=1 injector fields until the injectors are quickly shut off. At S=500, an n=0 component arises due to relaxation during sustainment. As S is increased further, the ratio of n=0 (equilibrium) fields to n=1 (injector) fields increases. The effects of a thin insulating boundary layer on the plasma decay time are also discussed.

Initial studies of steady inductive helicity injection on the HIT-SI experiment

The helicity-injected torus (HIT-SI) is designed to produce a "bow tie" spheromak, formed and sustained by steady inductive helicity injection (SIHI) current drive (Jarboe, 1999). SIHI is implemented via two "helicity injectors." Each injector acts as a 180/spl deg/ segment of a reversed-field pinch (RFP), with a typical peak current of 11 kA and a peak flux of 0.5 mWb. The toroidal loop voltage, toroidal injector plasma current, and toroidal flux of a single injector all oscillate sinusoidally at a frequency of 5 kHz and nearly in phase, so the single injector helicity injection rate and power input to the plasma are always positive. Operating the two injectors 90/spl deg/ out of phase in time provides nearly constant power input and helicity injection rate. To date, injector plasmas have been sustained in this manner for over 5 ms. An internal magnetic probe array has been installed in one of the injectors. Observations of the injector fields will be presented, illustrating the evolution of the field structure through the injector cycle.

Spheromak Fusion Propulsion for Future Solar System Exploration

Fusion propulsion for the exploration of the solar system is investigated. Minimum round-trip times for missions to Europa and Mars are given as a function of power/mass ratio. A preconceptual study of a spheromak-based, deuterium burning, fusion propulsion system is presented. The spheromak is sustained by inductive helicity injection with the diverted edge plasma becoming the rocket exhaust. Power/mass ratios of nearly 2 kW/kg appear possible, giving round-trip times of about 100 day for Mars and about one year for Europa. The vessel mass is 540 t not including fuel, a size suitable for human living. The I S P is optimized for a trip to Europa and a trip to Mars and was found to vary between 10,000 to 40,000 s.

Edge plasma characteristics in the helicity injected torus (HIT-II) spherical tokamak

The helicity injected torus (HIT-II) device is a spherical tokamak capable of both inductive (Ohmic) and co-axial helicity injection (CHI) current drive. The HIT-II plasma edge, in both Ohmic and CHI discharges, has been characterized using a triple Langmuir probe. An Ohmic discharge develops in two phases, a slide-away phase followed by a normal Ohmic discharge. During the normal Ohmic discharge, the floating potential is negative, just as in a conventional large-aspect-ratio tokamak. The plasma density increases sharply from the plasma edge into the centre. The auto-power spectrum of Ohmic plasma edge fluctuations shows a nearly constant auto-power at low frequencies, with auto-power decreasing at higher frequencies, similar to observations in conventional large-aspect-ratio tokamaks. In HIT-II CHI discharges, the magnetic field lines at the plasma edge are clearly connected to the injector electrodes, as expected. However, the time-evolution of the floating potential in the core plasma is significantly different from that of the edge, which may indicate a decoupling of the core plasma from the CHI electrodes. Finally, the fluctuations at the edge of high-performance CHI discharges exhibit a coherent oscillation at a frequency similar to that of the observed n = 1 mode.

Current drive experiments in the helicity injected torus (HIT-II)

The Helicity Injected Torus [HIT-II: T. Jarboe et al., Phys. Plasmas 5, 1807 (1998)] is a low-aspect-ratio tokamak capable of both inductive (ohmic) and Coaxial Helicity Injection (CHI) current drive. HIT-II is modest in size (major radius R=0.3 m, minor radius a=0.2 m, and on-axis toroidal field of up to 0.5 T), but has demonstrated 200 kA of toroidal plasma current, using either CHI or induction separately. The loop voltage, boundary flux, and plasma equilibrium are controlled by a real-time flux feedback system. HIT-II ohmic plasmas exhibit reconnection events during both the current ramp-up and decay, events that relax the current profile while conserving the magnetic helicity. A new operating regime for CHI plasmas, using a double-null divertor (DND) boundary flux, has been explored. DND CHI plasmas exhibit good shot-to-shot reproducibility, low impurity content, minimal shorting current in the absorber region, and EFIT-reconstructed equilibria consistent with significant closed-flux core regions [EFIT: L. Lao et al., Nucl. Fusion 25, 1611 (1985)]. HIT-II DND CHI discharges also exhibit a continuous n=1 mode at the outer midplane, a mode that has been correlated experimentally with current-profile relaxation. A detailed explanation of helicity injection current drive has been developed, which is consistent with experimental observations of HIT and HIT-II discharges. According to this mechanism, asymmetric distortion of the n=1 mode structure generates current drive in the core plasma by dynamo action, relaxing the CHI-driven current profile.