Physics of the Current Injection Process in Localized Helicity Injection Edward Thomas Hinson Pegasus Toroidal Experiment University of Wisconsin Madison 57 th American Physical Society Division of Plasma Physics Meeting Nov 215 University of Wisconsin-Madison PEGASUS Toroidal Experiment
Local Helicity Injection (LHI) is a Promising Non- Solenoidal Tokamak Startup Technique Current injected in plasma edge region Plasma startup and current growth.2 I p.18 MA (I inj = 5 ka).15 I p I p [MA].1.5 Local Helicity Injectors. 2 25 3 Time [ms] I inj 35 65358 Unstable current streams form tokamak-like state via Taylor relaxation Appears scalable to MA-class startup
Injector Impedance Relates Key Figures of Merit The simple model for helicity injection posits two I p limits related to the injector circuit Helicity balance limit depends on injector voltage V inj : I p A p # 2π R η V ind + A INJB φ,inj % $ Ψ T V inj Taylor relaxation limit depends on current I inj : & ( ' I p f ( ε,δ,κ) κ A p I TF I inj 2π R w Injector impedance describes relationship b/w I inj and V inj Determined by plasma physics Determines feasibility and power requirements for scaling up LHI
Edge Current Injection is Straightforward Conceptually Injection in Pegasus accomplished with arc plasma guns 2-stage circuit: bias and arc circuits daisy chained Voltage (~1 kv) is determined by plasma physics ARC INJECTION D 2 Arc Plasma Beam Drift Space, B.1 T Arc Cathode Arc Anode / Injection Cathode Vacuum Vessel / Injection Anode
Double Layer Sheath: A Promising Framework for Understanding Injector Impedance Two space-charged layers sandwiched to each other Width of space charge set by plasma, order λ De Double Layer Characteristics J = 4 9 1.865ε! 1+ m e # " m i $! & 2e $ # & %" m e % 1 2 V 3 2 2 l DL Charge density 2 l DL = ( λ De χ) 2 3 2 I ~ n DL V Electric Field Potential
I-V Characteristics Show 2 Regimes Typical I-V relationship shows two power law regimes, I inj ~V inj 3/2, V inj 1/2 Ip [ka] 6 4 2 1 4 6 4 I INJ [A] V INJ [V] 2 1 4 2 16 17 18 19 Time [ms] 2 I INJ [A] 1 3 1 2 2 6 4 2 V 1/2 V 3/2 4 6 8 2 4 6 8 1 1 V INJ [V]
Injector Impedance Has Fueling Dependence Deuterium gas flow rate into the source plasma scanned I inj, V inj I inj /V 1/2 increases with gas flow Arc Plasma I inj [A] 1 6 5 4 3 2 D 2 Flow Rate [Torr-L/s] 27 23 19 16 14 72 ~V 3/2 ~V 1/2 6 5 5 6 7 8 1 2 3 4 5 6 7 8 1 V inj [V]
1: Expanding Double Layer Yields I~n DL V 1/2 Simulations* find when V DL T e >>1: l DL ~ λ De V DL T e l DL λ De Expected I-V relation is: I inj ~ n arc V inj V DL T e Arc Plasma n arc ~ n DL Beam Double Layer *Hershkowitz 1985, Goertz 1975,1978, Benilov 29, R. A. Smith, Physica Scripta, 1982
2: Beam Neutralization Yields I inj ~n edge V inj 1/2 Electron beam propagation requires drift space ions neutralize electrons: n b n i Typical beam values imply beam density n b ~1 18 m -3 - comparable to edge density n edge! Assume drift space has same density as edge: n i n edge I inj = n b ev e A inj n i e 2eV inj m e A inj ~ n edge V inj I inj ~ n edge V inj
Impedance Model Based on Density Limits Created Minimum of both limits is applicable: Sheath expansion: I inj ~ n arc V inj Quasineutrality: I inj ~ n edge V inj Impedance Model: n b I inj = Min[n edge, βn arc ]e 2eV inj A inj m e βn arc n edge
n edge : n arc : Ohmic Plasmas Created to Test Model via Measured n edge, n arc Measured with Langmuir probe behind injector limiter Controlled with edge fueling Measured via Stark broadening of H-δ in arc channel Controlled with injector fueling Langmuir Probe Scraper Limiter Limiter Spectrometer
n arc Scanned Arc density n arc scanned Entire scan consistent with sheath expansion: n b ~βn arc where β=1/85 βn arc n b n edge 12x1 18 1 n edge n b 12x1 18 1 Density [m -3 ] n b [m -3 ] 8 6 4 2 n b =n arc /85 8 6 4 2 n edge [m -3 ] 2 4 6 8 1x1 21 n arc [m -3 ]
n edge Scanned at constant n arc Increasing n b at low n edge n b Saturation at n b =n arc /85 1x1 18 βn arc n edge n b [m -3 ] 8 6 4 2 n arc /85 2 4 6 8 1 12 14x1 18 n edge [m -3 ]
Interferometer Line-Averaged Density Expected to Trend with n edge Interferometer captures linear behavior at low n edge n b Saturation at n b =n arc /85 βn arc n edge Ip [ka] 12kA 8 4 4x1 18 n b [m -3 ] 3 2 1 n arc 3x1 21 m -3 16 18 2 22 Time [ms] 24 26ms 1 2 n e [m -3 ] 3 4x1 18
NIMROD Simulations Show Reconnecting Streams in Edge NIMROD shows* I p growth via intermittent reconnection Coherent current streams exist in edge throughout discharge Adjacent passes reconnect to inject rings into core Poloidal flux buildup and I p multiplication results Injected current-ring 2.91ms 2.93ms 2.94ms 2.95ms *J. O Bryan, PhD Thesis, UW Madison 214
Connection between Loop Creation, Bursts Bursts associated with coherent stream, current buildup I p [ka] 12 8 4-2 16 18 2 22 24ms -3 Time [ms] What could MHD say about existence of beam in edge? 3 2 1-1 Outboard Probe Signal [T/s] 2.91ms 2.93ms Injected current ring 2.94ms 2.95ms
Hypothesis: db/dt on PDXs Comes from Whirling (Infinite) Line Source Assume remote, circular stream rotation ΔB = µ I 2πr 1 µ I 2πr 2 = db dt µ I 2π ( r 1 r 2 ) dt µ I! ( r1 r! 2 ) µ I ( r 2πr 1 r 2 2πr 2 1 r 2 )cos(θ) cos(θ) r 2 db dt µ I cos(2π ft arctan(z / R)) 2πrf 2π R 2 + Z 2 db/dt structure looks like tumbling dipole db dt B R probe Z probe Z However, probes measure d(b z )/dt, not total db/dt R
Hypothesis: db/dt on PDXs Comes from Whirling (Infinite) Line Source Hypothesized db z /dt: db z, probe dt = µ Ir motion f cos[2π ft 2arctan[ z probe Z stream r probe R stream ]] ( z probe Z stream ) 2 + ( r probe R stream ) 2.5 m PDX-5: PDX-6: 4-lobed, fall-off is 1 r 2. m PDX-7: PDX-8: PDX-9: -.5 m.5 m 1. m
Fit to Data Looks Promising PDX5 PDX6 PDX7 PDX8 PDX9 T/s T/s db z, probe dt = Time [μs] µ Ir motion f cos[2π ft 2arctan[ z probe Z stream r probe R stream ]] ( z probe Z stream ) 2 + ( r probe R stream ) 2 R stream Z stream r motion.58m -.8m 1cm
Model Inverts for R(t), Z(t) Phase difference of 2 signals is Δϕ = 2arctan[ z probe1 Z stream r probe1 R stream ] 2arctan[ z probe2 Z stream r probe2 R stream ] The ratio of amplitudes of 2 signals ( ) 2 + ( r probe2 R stream ) 2 ( ) 2 + ( r probe1 R stream ) 2 T = z Z probe2 stream z probe1 Z stream 2 equations, 2 unknown R, Z of stream: ( ) ( ) T +1 T Δzsin Δϕ / 2 R stream = r p ± T ± 2cos Δϕ / 2 Z stream = z 2 T cos Δϕ ( )( z 1 + z 2 ) + z 1 T 2 ± T T 1 ( )Δzcos Δϕ / 2 T 2 2cos( Δϕ)T +1 ( )
R stream (t), Z stream (t) is Output Combine with uncertainty to yield small R,Z region σ T Z Signal origin appears localized σ Δϕ R
Managing Plasma-Material Interaction is a Formidable Challenge Injector requirements include V inj > 1 kv Large A inj, J inj Δt pulse ~ 1-1 ms Minimal PMI all adjacent to tokamak LCFS Significant evolution of design to meet physics challenges ~3x improvement in V inj, Δt pulse
Spots Move and Interact with Injector Structures Breakdown in the presence of plasma occurs ~1 5 V/cm At 1 18 /m 3, 1eV plasma, this is ~1kV Cathode spots, when ignited, roam cathode surface Interaction with insulators cases outgassing, damage Motion in field can potentially be controlled
Cathode Spot Motion in a Field Spot motion occurs in j x B direction, subject to angular displacement, ϕ No consensus model for ϕ exists
Barengoltz* Provides a Model for Motion in Arbitrary B Field Based on return currents seen in simulations New spots arise due to preferential bombardment by returning electrons Small spots have r<<r, Large spots have r=r φ arctan ( ϱ sin( θ B )) 1 2 ϱ ρ 1 *Zh. Tekh. Fiz. 68, 6 64 (June 1998)
Conical Frustum Design Implemented to Mitigate Cathode Spot Damage Conical shape used to induce inward motion of spots Self-magnetic field in Pegasus pushes spots outward radially Self Field Motion Acute angle motion Numerical approach necessary to balance these tendencies Heuristics are rendered as:! r ' = ρ ˆb ˆn ˆn ˆb ( ) ϱ ( ) + ˆn ˆb
Motion ALWAYS Outward for Concave Shapes 6834 I inj =19A
Convex Shape MIGHT Have Inward Motion! The sign of r ' = ϱ ρ ( ˆb ˆn ˆn ˆb ) + ˆn ˆb gives spot radial motion Frustum Pitch [ ] 9 75 6 45 3 15 Case 1: ϱ=1/2 Outward Radial Motion ( ) 1. 1.5 Frustum Radius [cm] Frustum Pitch [ ] 9 75 6 45 3 15 Case 2: ϱ=1 Inward Radial Motion 1. 1.5 Frustum Radius [cm]
Motion is Inward for Convex Cathodes in a Certain Interval 61632 I inj =15A ϱ=1
Summary Limits to max I p in LHI depend on V INJ, I INJ, and are related by I inj = min[n edge, βn arc ]e Initial model to understand MHD was created and suggests an oscillating, coherent beam Injector design improvements are allowing access to higher power operations 2e m e V inj A inj Reprints: Funded by grant DE-FG2-96ER54375 Dept. Engineering Physics Contact: ehinson@wisc.edu