D.J. Schlossberg, D.J. Battaglia, M.W. Bongard, R.J. Fonck, A.J. Redd University of Wisconsin - Madison 1500 Engineering Drive Madison, WI 53706
Concept Overview Implementation on PEGASUS Results Current areas of investigation Summary
Solenoid-free startup and ramp-up have been identified by FESAC as critical ST issues (FESAC TAP report) Solenoid-free startup with point-source helicity injection significantly extends the PEGASUS operating space Saves limited Ohmic transformer flux May enable high-i N, high-β studies on PEGASUS Point-source helicity injection is flexible Gun assemblies can be placed at convenient locations Presently being studied on PEGASUS (to date: I p up to 0.17 MA)
Helicity describes linking of magnetic flux K = 2Φ i Φ j Φ j Total helicity within a bounded volume Φ i K = N N i=1 j=1 L i, j Φ i Φ j V = A B d 3 x Current along B field = helicity Current drive = helicity injection Berger, M. Plasma Phys. Controlled Fusion 41, 1999
Total helicity in a tokamak geometry: K = V ( A + A vac ) ( B B vac ) d 3 x dk dt = 2 V ηj B d3 x 2 ψ t Ψ 2 A ΦB ds Resistive Helicity Dissipation E = ηj much slower than energy dissipation (ηj 2 ) Turbulent relaxation processes dissipate energy and conserve helicity AC Helicity Injection: DC Helicity Injection: K AC = 2 ψ t Ψ = 2V loop Ψ K DC = 2 A ΦB ds = 2V inj B A inj
Non-solenoid startup is a critical issue for future long-pulse STs Would extend efficiency of OH drive and provide j(r) modification on present experiments that already have a central solenoid Plasma gun point-source DC helicity injection tested on Pegasus Low impurity, high J inj source Scalable design flexible & compact Molybdenum Cathode - Anode Molybdenum Washers Molybdenum Cathode Anode D 2 gas V bias + Boron Nitride Washers V arc + Anode Gun
Inboard Divertor Gun Injection Outboard Midplane Gun Injection Anode Plate Spherical Anode Radial Plasma Guns Axial Plasma Guns R gun = 16 cm, Z gun = - 75 cm N.W. Eidietis UW-Madison Ph.D thesis, 2007 R gun = 70 cm, Z gun = - 20 cm D.J. Battaglia UW-Madison Ph.D thesis, 2009
Conditions for relaxation to occur: B v : low to allow null formation B TF : high to increase helicity injection B v, B TF : tokamak equilibrium - force balance, q a B v /B TF : avoid collision with injector hardware Consistent with experimental observations divertor injection: center-post limited discharges relaxation coincides with reversal of central poloidal flux midplane injection: model of perturbed magnetic field shows null in relaxed cases central column flux Current Divertor injection 60kA I p 40 I inj 20 0 ψ 200 pol I p /I inj 100 0-100 20 22 24 2628x10-3 time (s) Midplane injection 20A 15 10 5 0 current multiplication See D.J. Battaglia, et al., J. Fusion Energy, 28 (2009) 140-3
Open field line current M = G Injected current perturbs vacuum magnetic field Current multiplication: M I φ /I inj Tokamak-like plasma M > G Plasma expands inwards to fill the volume while connected to guns Limits dictated by helicity and Taylor relaxation Decaying plasma Stochastic magnetic fields heal into closed magnetic surfaces
Helicity balance in a tokamak geometry: dk dt = 2 V ηj B d3 x 2 ψ t Ψ 2 A ΦB ds Assumes system is in steady-state (dk/dt = 0) I p limit depends on the scaling of plasma confinement via the η term Taylor relaxation of a force-free equilibrium: B = µ 0 J = λb λ p λ edge Assumptions: µ 0 I p Ψ µ 0 I inj 2πR inj wb θ,inj Driven edge current mixes uniformly in SOL Edge fields average to tokamak-like structure V eff I p A p 2πR 0 η N inja inj B φ,inj Ψ εa I p f p I TF I inj G 2πR edge w A p Plasma area ( V + V ) ind eff V bias f G Plasma geometric factor I TF Toroidal field current w Edge width 1/ 2
Estimated plasma evolution Anode I p max Helicity limit I TF = 288 ka V bias = 1kV V ind = 1.5 V I inj = 4 ka w = d inj L-mode τ e Plasma guns Time Relaxation limit Total loop voltage from relaxation and PF ramp Recent experimental campaign: Testing utility and validity of this simple helicity/relaxation model
V bias = 1200 V 900 V Relaxation limit 120 V With guns, need sufficient helicity (i.e. V bias ) to reach the relaxation limit 1 Can confirm relaxation limit by adding OH drive as helicity source All three discharges have the same I inj and B v evolution 1 D.J. Battaglia, et al., Phys. Rev. Lett. 102 (2009) 225003
εa I p f p I TF I inj G 2πR edge w 1/ 2 I inj At each R 0, max. I p achieved scales as I inj 1/2 K inj insufficient to drive some discharges to limit as plasma expands Scan I inj : 1-5 ka I TF = 288 ka 3 plasma guns: defines w Assume plasma geometry (thus, εa p / R edge ) fixed at given R 0
Relaxation I p limit I TF 1/2 Supported by shot-to-shot comparisons Factor of two range in I TF Difficult to conclusively demonstrate scaling Limited range of I TF that produce quality discharges Plasma parameters depend on I TF Particle confinement decreases Energy confinement may decrease q is lower different equilibrium shape εa I p f p I TF I inj G 2πR edge w 1/ 2 Discharges with same I inj, V bias I TF
εa Relaxation limit predicted to scale as w -1/2 I p f p I TF I inj G 2πR edge w Data suggests w N gun D gun Likely due to alignment of plasma guns with flux surfaces w may also be related to edge instabilities, turbulence, drifts, etc. Anode 1/ 2 1 w w 3 guns
Orientation of gun array matched to edge field alignment Re-orientation is equivalent to a reduction in current channel width Experiments show increased relaxation limit Anode 140 After alignment Before alignment 120 w ka 100 80 60 40 20 0 0.4 3 guns 0.5 0.6 m 0.7 0.8
80 ka target handoff to OH drive Best coupling achieved when OH drive applied shortly after gun turnoff 150 ka with 18 mv-s ~ 50% flux savings Extending operation space - No significant MHD during Ohmic phase - Unlike OH only, where large scale n=1 activity limits plasma evolution - Equilibrium reconstruction of gun created plasmas show very low l i ~ 0.2-0.3, and hollow J(r)
Estimated Estimated Slower PF ramp Plasma detaches at 29.4 ms Faster PF ramp Plasma detaches at 25.3 ms After detachment, current drive is purely inductive and MHD activity is reduced.
What determines λ edge and λ p? Edge current measurements with probes Larger range of I TF to test scaling Re-tilted guns How does τ e scale with I p? Thomson scattering Increase V bias to achieve larger I p What determines Z inj? Filament path length and modeling Tokamak-like plasma properties: T i, T e Spectrometer, Thomson scattering I p (MA) 0.3 0.2 0.1 0.0 single gun three guns new geometry larger guns 2007 2008 2009 2010 year (Proposed) increased TF, V bias
Outboard midplane gun startup results show great promise I p ~ 0.17 MA achieved with simple 3-gun array and PF induction Helicity & Relaxation limits being identified to guide design to higher current Simple dc relaxation-helicity conservation model describes macroscopic scaling of current limit Many outstanding questions: λ edge, Z inj, confinement, etc Full understanding at microscopic level (e.g.. Intermittent MHD) will require deeper analysis (i.e. NIMROD) Pegasus goal: ~0.3 MA non-solenoidal target & hand-off to RF heating & growth Allows validation of understanding for projection to larger facilities (e.g.. NSTX up to MA)