IMPROVED CONFINEMENT OF C-2 FIELD-REVERSED CONFIGURATION PLASMAS H. GOTA,a* M. TUSZEWSKI,a E. TRASK,a E. GARATE,a M. W. BINDERBAUER,a T. TAJIMA,a L. SCHMITZ,a,b B. H. DENG,a H. Y. GUO,a S. AEFSKY,a I. ALLFREY,a D. BARNES,a N. BOLTE,a D. Q. BUI,a F. CECCHERINI,a R. CLARY,a K. D. CONROY,a M. CORDERO,a S. A. DETTRICK,a J. D. DOUGLASS,a P. FENG,a E. GRANSTEDT,a D. GUPTA,a S. GUPTA,a C. HOOPER,a J. S. KINLEY,a K. KNAPP,a S. KOREPANOV,a A. LONGMAN,a R. MAGEE,a R. MENDOZA,a Y. MOK,a A. NECAS,a S. PRIMAVERA,a S. PUTVINSKI,a M. ONOFRI,a D. OSIN,a N. RATH,a T. ROCHE,a J. ROMERO,a N. ROSTOKER,a J. H. SCHROEDER,a L. SEVIER,a A. SIBLEY,a A. SMIRNOV,a Y. SONG,a L. C. STEINHAUER,a M. C. THOMPSON,a T. VALENTINE,a A. D. VAN DRIE,a J. K. WALTERS,a W. WAGGONER,a X. YANG,a P. YUSHMANOV,a K. ZHAI,a and TAE TEAM a
Tri Alpha Energy Inc., P.O. Box 7010, Rancho Santa Margarita, California 92688 University of California, Los Angeles, Department of Physics and Astronomy, Los Angeles, California 90095
b
Received October 29, 2014 Accepted for Publication February 16, 2015 http://dx.doi.org/10.13182/FST14-871
C-2 is a unique, large compact-toroid (CT) device at Tri Alpha Energy that produces field-reversed configuration (FRC) plasmas by colliding and merging oppositely directed CTs. Significant progress has recently been made on C-2, achieving ,5 ms stable plasmas with a dramatic improvement in confinement, far beyond the prediction from the conventional FRC scaling. This stable, longlived FRC plasma state is called the high-performance FRC (HPF) regime. The key approaches to achieve the HPF regime are as follows: (i) dynamic FRC formation by collision/merging of super-Alfve´nic CTs, (ii) effective control of stability and transport by end-on plasma guns and neutral-beam (NB) injection, and (iii) active wall conditioning using titanium and lithium gettering systems. Moreover, further improvement in FRC confinement has been obtained with improved open-field-line plasma properties such as a lower fluctuation level, reduced
transport rates in radial/axial directions, and lower background neutral density as well as recycling. This open-field-line plasma improvement, mainly obtained by higher magnetic fields in the formation and mirror-plug sections, allows for better NB coupling to the core-FRC plasma. In the recent HPF regime there is a sufficiently large fast-ion population that appears to improve FRC confinement properties as well as stability; the FRC particle and global energy confinement times both increased by ,30% and ,80%, respectively, compared to that of the previously obtained HPF regime. KEYWORDS: field-reversed configuration, compact toroid Note: Some figures in this paper may be in color only in the electronic version.
*E-mail:
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C-2 FIELD-REVERSED CONFIGURATION PLASMAS
I. INTRODUCTION
A field-reversed configuration (FRC) is a high-beta compact toroid (CT) which has closed-field-line and open-field-line regions of poloidal axisymmetric magnetic field with no or small self-generated toroidal magnetic field.1,2 The beta value of FRCs is nearly unity: ,b. 52m0 , p . /B2e ,90%, where ,p . is the average plasma pressure and Be is the external magnetic field. The edge layer outside of the FRC separatrix coalesces into jets beyond the FRC length, providing a natural divertor, which may allow extraction of energy without restriction. Another attractive feature of the FRC is its potential for a fusion reactor with low-cost construction due to the simple geometry, and FRCs may also allow the use of advanced, aneutronic fuels such as D-3He and p-11B. The C-2 device is a large theta-pinch, CT-merging system, built at Tri Alpha Energy to form relatively high flux, high temperature FRC plasmas.3,4 Studying aspects of FRC plasma sustainment by neutral-beam (NB) injection and additional particle fueling is the main goal of the C-2 experiments. Figure 1 illustrates typical FRC magnetic flux and density contours in the C-2 device. These contours are obtained from a 2-D magnetohydrodynamic (MHD) numerical simulation performed with the LamyRidge equilibrium code.5 The C-2 device, as shown in Fig. 1, consists of a central confinement region surrounded by two u-pinch formation sources and two divertors. The stainless steel confinement chamber approximately conserves magnetic flux on the timescale of the experiment. The formation tubes are made of quartz. A set of DC-magnets generates a quasi-static axial magnetic field, Bz, throughout the device. The typical magnetic field is Bz,0.1 T in the confinement region with an end-mirror ratio of ,3.5. There are magnetic mirror-plugs in between the formation and the divertor sections at each side that can produce a strong magnetic field (Bplug) up to ,2 T, which corresponds to a plug-mirror-ratio (Rp 5 Bplug/Bz) of ,20. The mirror plugs play an important role of controlling the openfield-line plasma confinement. S. Divertor
Radius (m)
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The typical FRC energy confinement is largely determined by particle loss. Particles diffuse primarily radially out of the separatrix volume, and are then lost axially in the edge layer. Accordingly, the FRC confinement depends on the properties of both closed and open field line regions; both regions are important and control of the open-field-line sheath is beneficial for the FRC confinement. Thus, AMBAL-type plasma guns6,7 and magnetic mirror-plugs were installed in each side of C-2 divertors (Fig. 1) to explore radial electric field control in the FRC edge layer. The plasma guns as well as the mirror-plugs have many benefits such as improved FRC formation, edge layer confinement, particle refueling, stability through line-tying to the gun-electrode, neutral gas control, radial electric field control of the FRC rotation, and creation of E6B velocity shear. In C-2, a high-performance FRC (HPF) equilibrium state has been produced by dynamically colliding and merging two oppositely directed CTs (Refs. 3 and 4), and by combining effects of effective wall-conditioning, of biasing edge plasma near the FRC separatrix from the plasma guns, and of NB injection.8,9 Recently, further progress on the HPF performance has been made by improving open-field-line plasma confinement with stronger magnetic-mirror fields including formation sections. In this paper, C-2 operating conditions and characteristics of the HPF regime are described in Sec. II. Further improvement of the HPF regime, FRC global power balance analysis, and the HPF confinement properties are discussed in Sec. III. Results are summarized in Sec. IV. II. C-2 OPERATING CONDITIONS TO ACHIEVE HPF REGIME
Key approaches to achieve HPF operating conditions are as follows: (i) dynamic FRC formation by collision/ merging of super-Alfve´nic CTs, (ii) effective control of stability and transport by end-on plasma guns and NB injection, and (iii) active vessel-wall conditioning using titanium and/or lithium gettering systems.
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Fig. 1. Sketch of FRC magnetic topology and density contours in the C-2 device, simulated by the 2-D MHD LamyRidge equilibrium code. 2
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line-tying to the gun electrodes, aided by an axial magnetic field of ,0.5 T created by the gun magnet. The partial line-tying of the n51 mode requires sufficiently low sheath resistances, which are achieved in the C-2 device with sufficiently large gun-plasma densities (a few times 1018 m23) relative to the FRC edgelayer densities (, 1019 m23). The C-2 NBs (20 keV hydrogen, up to 4 MW total, ,2.5 MW trapped on average) are injected tangentially to the FRC current (co-injection), with an average radial impact parameter of 0.19 m which permits current drive. The fast ions, created primarily by charge exchange, have betatron orbits that add to the FRC azimuthal current, and a sufficiently large fast-ion population improves FRC stability and confinement properties significantly. C-2 HPF plasma parameters obtained through dynamic formation/merging are suitable for NB capture (shinethrough and first orbit losses , 15% initially) and for fastion confinement (slowing down time , FRC lifetime). Thus, NBs improve FRC performance synergistically with plasma guns under HPF conditions. III. IMPROVEMENT OF HPF REGIME
An example of HPF discharges, time evolutions of excluded-flux radius (rDf , rs: separatrix radius), is shown in Fig. 2; data sets obtained in 2012 and 2014 are labeled “HPF12” and “HPF14”, respectively. There are clearly different characteristics between the HPF12 and the HPF14 regimes; the major improvement of the HPF14 regime is largely due to the open-field-line plasma improvement. The key differences of C-2 operating conditions and the HPF plasma properties between the two data sets are summarized in Table I. The open-field-line plasma improvement is obtained by stronger magnetic fields in the formation sections as well as the magnetic mirror-plug regions in addition to lithium-wall conditioning on the confinement vessel. As illustrated in Fig. 1, higher formation and mirror-plug 0.4 HPF14 shots:
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A typical C-2 merged-FRC plasma state, produced by field-reversed theta-pinch (FRTP) dynamic formation, translation, and collision processes, exhibits the following FRC properties: radius ,0.4 m, length ,3 m, rigid-rotor poloidal flux up to ,10 mWb, total temperature (Ti+Te) up to ,1 keV, electron density ,361019 m23, and external axial magnetic field ,0.1 T. Note that recent HPF discharges tend to have somewhat smaller plasma dimensions and densities. In order to reduce impurity content and control recycling in C-2, wall conditioning by titanium and/or lithium coatings has been applied to the stainless-steel confinement and divertor inner-walls. Reducing background neutrals is a key for NB injection into a target FRC for mitigating large charge-exchange losses. Both titanium/lithium gettering systems cover over 80% of the total surface area of the inner-wall. In typical C-2 FRCs, the dominant impurities without gettering are oxygen, carbon, and nitrogen, mainly coming out from the chamber walls and formation sections. Both gettering techniques have significantly reduced the neutral recycling, based on Da emissions (l ,656 nm), by a factor of 4–5 compared to those without wall conditioning. Survey spectrometers also indicate a large reduction in impurity contents by gettering. Recent progress in improved confinement of the HPF regime was achieved with lithium wall conditioning, which reduced line-radiation due to being a low-Z material. The magnetic-mirror plugs (inner-diameter ,0.25 m and length ,0.35 m) between the formation regions and the divertors may improve the edge-layer particle confinement, thus core FRC particle confinement may also be improved. The mirror plugs are also important for neutral gas control. For ideal FRC formation all magnetic field lines within the quartz tube volume are passing through the mirror-plug without wall contact. In this case the high-density plasma flowing through the mirror plugs should provide efficient neutral ionization. The neutrals recycled from the diverted FRC exhaust plasma jets may not return to the confinement vessel. The neutrals associated with the plasma gun operation are mostly confined in the divertor. Two AMBAL-type plasma guns are mounted inside of both divertors, as shown in Fig. 1, and produce a hot (Te ,30–50 eV, Ti ,100 eV) tenuous (,1018 m23) plasma stream. The anode to cathode voltage difference is typically about 500 V, and the gun arc current is about 10 kA. The gun also creates an inward radial electric field (Er , 0) in the plasma stream, which is important and key for edge control via the open-field-lines. The –Er counters FRC typical spin-up in the ion diamagnetic direction and mitigates the toroidal n52 rotational mode.8,9 The plasma gun also produces E6B velocity shear just outside of the FRC separatrix, yielding improved FRC confinement properties and stability. Better plasma centering (less n51 wobble motion) is also obtained presumably from partial
C-2 FIELD-REVERSED CONFIGURATION PLASMAS
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Fig. 2. Time evolution of excluded-flux radius in HPF discharges obtained in 2012 and 2014 with different C-2 operating conditions, labeled HPF12 and HPF14, respectively. 3
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TABLE I Key C-2 Operating Conditions Underlying the HPF12 and HPF14 Data Sets and Resulting Characteristics of HPF Plasma Properties Data set Wall conditioning Confinement field, Be (T) DC-formation field, BFS (T) Mirror-plug field, Bplug (T) Density fluctuation levels in core/SOL regions Confinement FRC configuration lifetime (ms)
HPF12 Titanium , 0.1 , 0.05 0.5 –1.0 Low/moderate
HPF14 Lithium , 0.1 0.065 –0.08 1.5 –2.0 Low/low
Moderate 1.5 –3.0
High 3.0 –4.0
Configuration lifetime (ms)
4 Low BFS High BFS
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1 Bplug (T)
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Fig. 3. (a) Effect of magnetic mirror-plugs with low DCformation field (BFS ,0.05 T, black squares) and high DC-formation field (BFS . 0.065 T, red circles) conditions, and (b) time evolution of excluded-flux radius with various magnetic mirror-plug strengths under high BFS condition.
(0-D) global power balance model11 in order to derive transport timescales for HPF12 and HPF14 regimes. Evolution of the ion and electron thermal energies is measured in the experiment, while source and loss terms are estimated. Major heating terms include volumetric compression, ohmic heating due to resistive decay of the plasma current, and NB sources. Sinks consist of convective particle loss, heat loss due to conduction, and radiation. Estimation of plasma parameters is limited to the FRC core; the extent to which derived transport timescales represent core properties alone is an area of active research. Typical performance of both HPF12/14 discharges is listed in Table II. Here, conductive and radiative timescales are inferred from the ratio of thermal energies to the respective loss powers, while convection is directly estimated from measured changes in the electron inventory. In the HPF12 data set the fastest losses are clearly in the electron channel, with conduction and radiation playing dominant roles in the overall evolution of the discharge. HPF14 characteristics capture some of FUSION SCIENCE AND TECHNOLOGY
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∼0.4 T ∼1.0 T ∼1.6 T
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fields allow for more field-lines to squeeze into the divertor sections; in other words, better field-line mapping throughout the machine with less contact with the formation quartz-tubes and the necking/mirror-plug walls. Figure 3a shows the effect of magnetic mirror-plug fields under low DC-formation field (BFS,0.05 T, black squares) and high DC-formation field (BFS . 0.065 T, red circles; color online) conditions; all data were obtained with Li-gettering and each data point is averaged over at least 10 discharges under the same operating conditions. Under low BFS condition, there is no clear effect of the magnetic mirror-plug strength on plasma performance; while under high BFS conditions, as also shown in Fig. 3b, a clear improvement in FRC performance/lifetime can be seen with higher magnetic mirror-plug field strength. Higher magnetic fields in the formation/mirror-plug sections appear to improve the open-field-line/SOL plasma properties such as fluctuation levels and parallel transport; in turn it leads to improvements in the core plasma properties, including particle and energy confinement. The density fluctuation levels in the FRC core and SOL regions have been measured by Doppler backscattering (DBS) reflectometer system10 near the C-2 central region. Lower fluctuations outside of the FRC separatrix are identified with higher BFS and Bplug fields, which characterize the HPF14 regime. Overall confinement improvement provides for better NB coupling to the core plasma; thus, more fast-ions trapped/confined inside the FRC. In the HPF14 regime there is a sufficiently large fast-ion population that appears to increase the diamagnetic signals, as shown in Fig. 2, and further improve FRC confinement properties as well as stability. While in typical previous FRCs energy confinement is attributed largely to particle loss (and depends on the properties of both closed and open field line regions), in C-2’s HPF regimes the convective losses have been dramatically reduced rendering conduction the likely largest loss channel. Energy flows into and out of the FRC core have been estimated using a zero-dimensional
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TABLE II Convective, Conductive, and Radiative Energy Decay Times for Both Ion and Electron Channels Based on 0-D Power Balance Analysis in HPF12 and HPF14 Regimes* HPF12 Timescales at 1 ms Convection Conduction Radiation
Ions (1.0 kJ) 0.8 ms 5.8 ms —
HPF14
Electrons (0.1 kJ) 0.8 ms 0.15 ms 0.2 ms
Ions (1.6 kJ) 1.4 ms 9.3 ms —
Electrons (0.2 kJ) 1.4 ms 0.2 ms 1.6 ms
*The confined thermal energies for ions and electrons are also listed in parentheses.
the observed improvements in FRC plasma performance; particle confinement was improved, while radiation ceased to be a significant factor in power losses. All power loss terms reduced dramatically in the HPF14 regime, and with the improved transport timescales, the FRC plasma lifetime increased commensurately, as listed in Table I. The C-2 FRC global energy confinement times tE in HPF12 and HPF14 regimes are estimated and shown in Fig. 4 to compare with previously obtained C-2 FRC data sets.8 Note that for those data analysis and comparison under several different C-2 operating conditions, 2 different analysis time windows are selected: t50.1– 0.5 ms for short-lived C-2 FRCs (No Gun and Gun Only cases), and t50.5–1.5 ms for longer-lived HPF discharges (Gun+NBs and 2 Guns+NBs cases). All data set is shotaveraged with more than 10 similar discharges in the same operating condition. A dramatic improvement in FRC energy confinement time can be seen in Fig. 4; in particular, from HPF12 (tE,0.44 ms) to HPF14 (tE,0.80 ms) regimes. The impact of gettering material from titanium to lithium is clearly evident from the analysis of radiated power and associated timescale. Line
radiation from titanium decreased substantially, while further reductions in recycling may have also contributed to open-field-line plasma and core FRC improvements in the HPF14 regime. The FRC particle confinement times tN are also estimated in both HPF12/14 regimes and are compared in Fig. 5 with old FRC data sets, including previously obtained C-2 data as well as ones from other FRC devices (seen in Fig. 6 of Ref. 9). The abscissa is the conventional/empirical FRC scaling law, which approximately scales as R 2/rie, where R5 rs/!2 and rie is the ion gyroradius evaluated with Be. The tN values are the e-folding decay times of the FRC separatrix particle inventory and shot-averaged over many similar FRC discharges. The shot selection and the analysis time 2.5 C-2
FIX LSM LSX NUCTE
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Fig. 4. FRC global energy confinement times in different C-2 operating conditions. Each data set is shot-averaged. Analysis time windows for early C-2 FRCs (No gun and Gun only) and HPF shots (HPF, HPF12, and HPF14) are t ¼ 0.1–0.5 ms and t ¼ 0.5–1.5 ms, respectively. FUSION SCIENCE AND TECHNOLOGY
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Fig. 5. FRC particle confinement times in the C-2 device (circles) and in other FRC experiments. Each C-2 data set is shot-averaged under the same operating conditions as shown in Fig. 4. Note that analysis time windows for early C-2 FRCs (No gun and Gun only) and HPF shots (HPF, HPF12, and HPF14) are t ¼ 0.1– 0.5 ms and t ¼ 0.5–1.5 ms, respectively. Newly obtained data points of HPF12/14 are highlighted. 5
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windows are the same as FRC energy confinement analysis, as described above and shown in Fig. 4. Using a larger analysis time window (t50.5–1.5 ms) for HPF discharges results in lower values of tN and R 2/rie than those of using the old analysis time window (t50.1– 0.5 ms) in C-2. However, as can be seen in Fig. 5, a further increase in the C-2 FRC particle confinement time is obtained under the HPF14 regime; more specifically, the particle confinement times increased from ,1.54 ms (HPF12) to ,2.0 ms (HPF14) resultant from a large improvement of open-field-line plasma properties. Overall C-2 has demonstrated a dramatic improvement in FRC confinement properties, and the recent HPF14 data appears a factor of ,10 above the empirical FRC scaling laws.1,2,12 IV. SUMMARY
The C-2 device has been producing stable, long-lived high-performance FRC regimes with end-on plasma guns and with NB injection. A further improvement in the FRC confinement has recently been made in the HPF14 regime; it is strongly coupled to the improvement of open-fieldline/SOL plasma properties such as lower fluctuation levels, reduced transport rates, and lower background neutral density and recycling. This SOL plasma improvement, obtained by higher magnetic fields in the formation/mirror-plug sections and by Li-gettering, allows for better NB coupling to the core-FRC plasma; thus, more fast-ions are confined in the FRC, which appears to improve FRC confinement properties as well as stability. A zero-dimensional global power balance model was used to derive transport timescales for HPF12/14 regimes, and it shows that changes to the open-field-line plasma and boundary conditions are responsible for decreased losses across the board and increased FRC plasma lifetime. In the HPF14 regime FRC particle and global energy confinement times both increased by ,30% and ,80%, respectively, compared to those of the HPF12 regime. ACKNOWLEDGMENTS The authors wish to thank the entire TAE Team for their dedicated work and effort on the C-2 experiment, our Budker Institute colleagues for many key contributions to our experiment, and our shareholders, who enabled this exciting research effort.
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REFERENCES 1. M. TUSZEWSKI, “Field Reversed Configurations,” Nucl. Fusion, 28, 2033 (1988); http://dx.doi.org/10.1088/0029-5515/ 28/11/008. 2. L. C. STEINHAUER, “Review of Field-Reversed Configurations,” Phys. Plasmas, 18, 070501 (2011); http://dx.doi. org/10.1063/1.3613680. 3. M. W. BINDERBAUER et al., “Dynamic Formation of a Hot Field Reversed Configuration with Improved Confinement by Supersonic Merging of Two Colliding High-b Compact Toroids,” Phys. Rev. Lett., 105, 045003 (2010); http://dx.doi. org/10.1103/PhysRevLett.105.045003. 4. H. Y. GUO et al., “Formation of a Long-Lived Hot Field Reversed Configuration by Dynamically Merging Two Colliding High-b Compact Toroids,” Phys. Plasmas, 18, 056110 (2011); http://dx.doi.org/10.1063/1.3574380. 5. L. GALEOTTI et al., “Plasma Equilibria with Multiple Ion Species: Equations and Algorithm,” Phys. Plasmas, 18, 082509 (2011); http://dx.doi.org/10.1063/1.3625275. 6. G. I. DIMOV et al., “Production and Study of a Target Plasma Jet for an Open Confinement System,” Sov. J. Plasma Phys., 8, 546 (1982). 7. T. D. AKHMETOV et al., “Experiments with Dense Plasma in the Central Solenoid of AMBAL-M,” Fusion Sci. Technol., 43, 58 (2003). 8. M. TUSZEWSKI et al., “A New High Performance Field Reversed Configuration Operating Regime in the C-2 Device,” Phys. Plasmas, 19, 056108 (2012); http://dx.doi.org/10.1063/ 1.3694677. 9. M. TUSZEWSKI et al., “Field Reversed Configuration Confinement Enhancement Through Edge Biasing and Neutral Beam Injection,” Phys. Rev. Lett., 108, 255008 (2012); http:// dx.doi.org/10.1103/PhysRevLett.108.255008. 10. L. SCHMITZ et al., “Multi-Channel Doppler Backscattering Measurements in the C-2 Field Reversed Configuration,” Rev. Sci. Instrum., 85, 11D840 (2014); http://dx.doi.org/ 10.1063/1.4891415. 11. D. J. REJ and M. TUSZEWSKI, “A Zero-Dimensional Transport Model for Field-Reversed Configurations,” Phys. Fluids, 27, 1514 (1984); http://dx.doi.org/10.1063/1.864783. 12. A. L. HOFFMAN and J. T. SLOUGH, “Field Reversed Configuration Lifetime Scaling Based on Measurements from the Large Experiment,” Nucl. Fusion, 33, 27 (1993); http://dx. doi.org/10.1088/0029-5515/33/1/I03.
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