Study of the Hard X-rays from Superthermal Electrons in the HSX Stellarator A. E. Abdou, A. F. Almagri, D. T. Anderson, J. Radder, V. Sakaguchi, J. N. Talmadge HSX Plasma Laboratory, U. of Wisconsin, Madison
1. The Helically Symmetric 2. Particle Orbits in HSX 4. Initial Results g. Evidence for a Non-thermal h. Similar HXR Emission at Different Electron Population Resonance Locations in QHS Experiment (HSX) a. Particle Orbits in QHS a. Different Hard X-ray Characteristic in QHS d. Hard X-ray Intensity variation with Plasma 1000 1000 o 4.5 y = 230.32 - 0.0043 x dN/dE = 267- 0.0047 E 20 KeV electrons with 80 pitch angle, launched at = 0, 2 a. Machine Parameters and r/a = ½ 4 100 R2 = 0.9706 100 R = 0.953 and Mirror Density ECE TS Temperature = 232.55 +/- 1.85 keV Temperature = 212.766 +/- 1.63 keV 3.5 10 10 250 1800.0 3
Major Radius 1.2 m The hard x-ray spectrum for 401 dN/dE (Number/Kev)
1600.0 QHS 2.5 1 dN/dE (Number/KeV) 1 (keV)
QHS and Mirror, central heating 351 200 Anti_Mirror e
0.12 m 1400.0 2 T 3 shows: QHS Mirror 1.5 0.1 0.1 Volume ~.44 m 301 1200.0 0 500 1000 1500 2000 0 500 1000 1500 2000 1. Density of superthermal 150 1 Energy (KeV) Energy (Kev) Field periods 4 251 1000.0 • When electrons are launched at the inboard side (the top of magnetic well) electrons is higher in QHS than 0.5 1000 201 Counts 800.0 dN/dE = 151.15 - 0.0055 E axis 1.05 100 0 LFS HFS Number of Counts Numberof 2 they are passing particles in Mirror. 100 R = 0.9506 151 600.0 0 0.5 1 1.5 2 2.5 edge 1.12 • When they are launched at the outboard side (the bottom of the magnetic (count) dN/dE Temperature = 181.82 +/- 2.25 keV 2. Electrons are heated to 400.0 101 50 n , 1018 m-3 Coils/period 12 well) they are trapped with their orbits deviation from home flux surface e 10 higher energies in QHS than in 200.0 being small compared to Mirror and antiMirror cases. Mirror 51 • Comparison of ECE and TS data suggests the B0 (on axis) .4-.6 T 0 0.0 dN/dE (Number/KeV) 1 Central 1.25 T Max • No or minor difference in hard x-ray emission is expected between 1 1.00E+10 2.10E+11 4.10E+11 6.10E+11 8.10E+11 1.01E+12 1.21E+12 0.E+00 1.E+11 2.E+11 3.E+11 4.E+11 5.E+11 6.E+11 7.E+11 8.E+11 9.E+11 existence of non-thermal electrons at lower density 3. The antiMirror case has a -3 0 100 200 300 400 500 600 700 800 -3 Density (cm ) inboard and outboard sides. Density (cm ) 0.1 very small signal Energy (Kev) plasmas. 0 500 1000 1500 2000 1- In QHS The HXR Intensity decreases with density. Energy (KeV) ECH Pulse Up to 50 • Discrepancy disappears near line averaged densities length (up to msec. 2- While in the Anti-Mirror case we have very low count rate. 12 -3 now) b. Particle Orbits in Mirror Property QHS Mirror 11 of ~1.7 - 2.0 10 cm . As predicted before from the energetic electrons drift orbit 3- Hard x-ray intensity is nearly flat at ne < 4 x 10 , then increases suddenly to 11 -3 Heating Power Up to 100 o 11 • See K. Likin’s poster for more information on ECE, analysis in QHS (at ne = 4 x10 cm ), there is nearly no 20 KeV electrons with 80 pitch angle, launched at = 0, Max. Intensity (number) ~ 351 ~ 151 a maximum at ne ~ 4.2 x 10 , and begin to decrease with increasing electrons (up to now) kW and r/a = ½ density. and K. Zhai for Thomson Scattering. difference in hard x-ray emission at different resonance Max. Energy (KeV) ~ 600 ~ 100 11 -3 location. 4- QHS and Mirror have similar behavior for ne > 5 x 10 cm . b. Magnetic Field Structure b. Hard X-ray Intensity Shows Improved e. Different Stored Energy Behavior in QHS and 5. Future Work Mirror Modes • When electrons are launched at the inboard side (top of the magnetic Confinement in QHS Over Mirror Mode well) they are passing particles. Similar to the QHS inboard case. a. Future Experiment b. Fokker-Planck Modeling • HSX is the worlds first 50 50 Quasi-Symmetric • When they are launched at the outboard side (bottom of the magnetic • HXR signal shows strong well) they are trapped with their orbits deviation from home flux surface 900 QHS Central Heating 45 •What is the effect of changing resonance location on HXR emission? Stellarator, based on a evidence of the existence of 10% Mirror Central Heating The CQL3D code being large compared to QHS (because of the asymmetry in the magnetic 800 40 40 At the same plasma density, investigate the hard x-ray emission at dominant n = 4, m = 1 superthermal electrons in QHS (total # = 3179) 700 35 - 3D, Multi-species, toroidal, fully relativistic code component of the ripples). Mirror (total # = 539.92) different resonance locations (LFS, Central, HFS) for QHS, Mirror and both QHS and mirror - Accepts the measured plasma parameters (T and n ) as simple input variables magnetic spectrum. • Different hard x-ray emission is expected in inboard and outboard sides. 600 Microwave Signal 30 30 antiMirror. e e configurations (central >( J )
p to calculate the >( J ) 500 p 25 • This symmetry can be mirror term (n = 4, m = Count (total in 5 mSec) 200 10 10 ray emission as density increases. - The diffusion coefficient as function of radius and energy is calculated in 0) B B 1 cosN m 20 KeV electrons with 80o pitch angle, launched at = 0, • The confinement of CQL3D using the 0 h 100 5 • All symmetry breaking and r/a = ½ superthermal electrons in •What is the effect of changing ripple amplitude on HXR emission? power deposition and wave electric fields calculated from ray tracing codes. In straight line coordinates 0 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 780 800 820 840 860 880 900 920 11 -3 11 -3 Investigate the hard x-ray emission in the Mirror mode for different terms below 1% of QHS is better than Mirror (10 cm ) (10 cm ) - The code includes highly benchmarked bremsstrahlung diagnostic e e average field. Time (mSec) ripple amplitudes (Mirror and antiMirror %). calculations. The line of site B B01h cos N m case. integrals measured by x-ray diagnostics are computed in CQL3D for direct 11 -3 •Is there any nonthermal component in the stored energy? • In QHS, the stored energy increases with density (ne < 4 x 10 cm ), then it comparison. Investigate the stored energy dependence on density and resonance - CQL3D has a limited applicability to model the Mirror and antiMirror Property QHS Mirror begin to decrease with further increase in density, and become flat for ne > 9 x location and compare it to the hard x-ray emission. 1011 cm-3. configurations. Max. Intensity ~ 391 ~ 102 What is the effect of changing the ECRH power level on the HXR • When electrons are launched at the inboard side (local maximum of 11 -3 The Marushchenko code decay time (msec) ~ 13.0 ~ 5.3 • In Mirror, the stored energy increases with density (ne < 9 x 10 cm ), and emission? - 5D Fokker-Planck, studies electron cyclotron resonance heating ECRH of c. Modes of Operation the magnetic field) they are trapped with their orbits deviation from become constant for n > 9 x 1011 cm-3. At fixed resonance location and plasma density, investigate the hard x-ray e fusion plasmas flux surface being large compared to QHS and Mirror cases. spectrum as a function of ECRH power level. • When electrons are launched at the outboard side (bottom of the - Periodic magnetic field magnetic well) they are in direct loss orbit. c. “Temperature” Evolution Shows Good f. Stored Energy may be Correlated with Hard X- c. Experimental method to Model - The solution for the distribution function is obtained by means of • Very low hard x-ray intensity is expected in both cases for antiMirror. conservative, finite difference, Confinement of Superthermal Electrons in the ray the Superthermal Electron two-step operator scheme. QHS Mode 20 Distribution Function 3. Hard X-ray Diagnostics 6. Conclusion 350 15 Another way to model superthermal electron distribution 9 8 300 Temperature (Kev) function is to use hard x-ray pulse height analysis • Hard x-ray analysis of the initial results up to H = 0.0065 G - 0.0393 7 10 2 Microwave Signal diagnostics. now show better confinement of superthermal 6 R = 0.9998 250 5 electrons in QHS compared to Mirror and 200 Solution procedures 4 5 antiMirror configuration. 3 T(Kev) 150 - Experimental data 2 StoredEnergy (Joules) H (Pulse Heigh in Volts)in Heigh (Pulse H • The future experimental work will involve 1 100 0 Two features of the data the modeling should reproduce 0 modeling the superthermal electron distribution Configuration Auxiliary Coil Dominant Feature 1.0E+10 2.1E+11 4.1E+11 6.1E+11 8.1E+11 1.0E+12 1.2E+12 1- The asymmetry in x-ray between small and large 0 200 400 600 800 1000 1200 50 function, investigating the hard x-ray emission in Currents G (Gain) -3 0 Density (cm ) large viewing angles. different magnetic configurations and QHS None Lowest neoclassical transport; Quasi- • Detector Type: CdZnTl 780 800 820 840 860 880 symmetry 2- The slope of the plot of the photon counts versus understanding the nonthermal component of the • Good energy resolution (3% – 10 %). Time (mSec) 11 -3 • In Mirror, stored energy increases with density for ne < 4.2 x 10 cm , MIRROR 3 coils on ends add to Neoclassical transport similar to Fast timing characteristics (rise time 0.05 – 0.5 s). In QHS, time evolution of the superthermal electron temperature deduced 12 -3 versus photon energy at each viewing angle stored energy. main; center 6 conventional stellarator and become constant for ne > 4.2 x 10 cm . dN(k / , ) d (k / , , P ,Z ) opposite • High x-ray stopping efficiency (Compact size 10 mm x 10 mm x 2 from HXR under the assumption of Maxwellian distribution, shows: - Bremsstrahlung emission a d 3P f (P, ) o o i v • The Fokker-Planck simulation will help us • Hard x-ray and stored energy change their behavior at the same density dk / dt p dk 'd o ANTI-MIRROR Opposite phasing to Similar neoclassical transport to mm). 11 -3 o understand the experimental results and calculate 1. Good confinement (i.e. ne ~ 4.1 x 10 cm ). - Bremsstrahlung cross-section mirror Mirror. Deep ripple on low-field side at P P// • No sensitivity to magnetic field (no magnetic shields required) ( ) how much energy is carried by superthermal ECH launcher f ( p) C e 2T 2T// • Operate at room temperature (no need for cooling) 2. High energy of superthermal electrons - Model electron distribution function N electrons during the ECRH discharges. • Fulfills our experimental needs.