Fast Ion Connement in the MST Reversed Field Pinch Gennady Fiksel B. Hudson, D.J. Den Hartog, R.M. Magee, R. O'Connell, S.C. Prager MST Team - University of Wisconsin - Madison Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas A.D. Beklemishev, V.I. Davydenko, A.A. Ivanov, Yu.A. Tsidulko Budker Institute of Nuclear Physics, Novosibirsk, Russia 47th APS DPP Meeting, Denver, CO, October 24-28, 2005
Motivation Neutral Beam Injection (NBI) heating of Reversed Field Pinch plasma. Low equilibrium magnetic eld - large Larmor radius of fast ions. Relatively large magnetic fluctuations can make the magnetic eld stochastic. How does it affect the connement of fast ions?
Outline Numerical tracing of stochastic magnetic eld lines and ion orbits. Injection of energetic neutral beam and measurement of the dynamics of fast ion content. Fast ion can be well conned even in the presence of stochastic magnetic eld. Explained by simple Ion Guiding Center island overlap model.
Madison Symmetric Torus (MST) Reversed Field Pinch Toroidal, current-carrying R = 1.5 m ; a = 0.5 m Density n ~ 1013 cm 3 Temperature Te up to1.5 kev
Resistive tearing modes are unstable in standard RFP plasma Multiple resistive tearing modes can exist q = rb t RB p q kib = 0 0.3 0.2 0.1 0.0 1,6 1,7 1,8 rational surfaces -0.1 0.0 0.2 0.4 0.6 0.8 1.0 r/a mode resonant with the equilibrium eld on rational surfaces. 0,n q = m n m - poloidal mode number n - toroidal mode number
Magnetic mode radial prole Radial Magnetic Field m = 1 B r (total) B (Gauss) n = 7 n = 6 n = 8 r/a
Single mode island safety factor q(r) w M = 4 m=1, n=6 b rn B ϑ r n q M Magnetic island is formed on a rational surface. Magnetic eld mapping is done with the code RIO. Cylindrical geometry. toroidal transit/π Isolated mode m=1, n=6, δb / B =1% - typical value for standard RFP plasma. r/a
Overlapping of multiple islands m=1 n=6 n=7 n=8 Radial prole of magnetic modes is calculated with the resistive MHD code DEBS (3D, cylindrical). Mode amplitudes normalized to experimental values at the wall. Islands are broad and overlap, the eld should be stochastic.
Field line mapping - magnetic eld is stochastic Magnetic mapping with code RIO in cylindrical geometry. m=1 n=6 n=7 n=8
Field line mapping - magnetic eld is stochastic Magnetic diffusion D m 10-4 m - diffusion length less than 1000 m or 100 toroidal transits. Fast particle (10 6 m/s) attached to eld line - expected connement time less than 1 ms. m=1 n=6 n=7 n=8
Fast ion orbits mapping - fast ions are well conned Full orbit ion motion in cylindrical geometry - code RIO Mapping of the position of Ion Guiding Center for longer than 100 toroidal transits. m=1 n=6 n=7 n=8
Schematics of the experiment and result Short pulse, 1.3 ms, of fast D neutrals injected into MST deuterium plasma. Tangential injection in co-direction. NBI 20A 25 kev PMT Lead shield 1.5 m scintillator B-408
Schematics of the experiment and result Short pulse, 1.3 ms, of fast D neutrals injected into MST deuterium plasma. Tangential injection in co-direction. Fusion d-d neutrons from fast ions/plasma ions collisions are measured by a scintillator detector The decay time is long. NBI 20A 25 kev Γ n n n i v σ dd (E ) V PMT Lead shield 1.5 m scintillator B-408
Modeling of fast ion connement 1 E Γ n n n i v σ dd (E ) V de dt dn dt = S n loss τ 3 2 4 1/ 2 Z e n Λ em ln( ) E 2 4 = me me + 2 3/ 2 1/ 2 4 2πε mee 3π m Te i m 0 i niz n e 2 i
Modeling of fast ion connement 1 E Γ n n n i v σ dd (E ) V de dt dn dt = S n loss τ 3 2 4 1/ 2 Z e n Λ em ln( ) E 2 4 = me me + 2 3/ 2 1/ 2 4 2πε mee 3π m Te i m 0 i niz n e 2 i
Modeling of fast ion connement 1 E Γ n n n i v σ dd (E ) V de dt dn dt = S n loss τ 3 2 4 1/ 2 Z e n Λ em ln( ) E 2 4 = me me + 2 3/ 2 1/ 2 4 2πε mee 3π m Te i m 0 i niz n e 2 i
Modeling of fast ion connement 1 E Γ n n n i v σ dd (E ) V de dt dn dt = S n loss τ 3 2 4 1/ 2 Z e n Λ em ln( ) E 2 4 = me me + 2 3/ 2 1/ 2 4 2πε mee 3π m Te i m 0 i niz n e 2 i
Connement of fast ions is much better than expected from simple estimates based on magnetic eld stochasticity. Why?
Ion orbits do not follow the eld lines Rotational transform of fast ion orbits is different from that of eld lines due to orbit drifts. 0.3 Magnetic eld safety factor q=1/6 corresponds to 6 poloidal transits per 1 toroidal transit q = rb t RB p q 0.2 0.1 0.0 1,6 1,7 1,8 0,n -0.1 0.0 0.2 0.4 0.6 0.8 1.0 r/a
Ion orbits do not follow the eld lines Rotational transform of fast ion orbits is different from that of eld lines due to orbit drifts. 0.3 Magnetic eld safety factor q=1/6 corresponds to 6 poloidal transits per 1 toroidal transit 25 kev ion orbit 5 poloidal transits per 1 toroidal transit q = rb t RB p q 0.2 0.1 0.0 1,6 1,7 1,8 0,n -0.1 0.0 0.2 0.4 0.6 0.8 1.0 r/a
Rotational transforms of fast ion orbits and eld lines are different due to orbit drifts Dene Ion Guiding Center (IGC) safety factor analogously to that of magnetic eld lines. Magnetic safety factor q M = rb φ /RB θ IGC safety factor q = rv φ IGC IGC /Rv θ
Rotational transforms of fast ion orbits and eld lines are different due to orbit drifts That changes the resonant interaction with magnetic modes and affects the onset of stochasticity. Magnetic resonances and islands IGC resonances and islands q M = rb φ /RB θ q = rv φ /Rv θ w M = 4 b rn B ϑ r n q M w = 4 v rn v ϑ r n q
Ion guiding center n = 5 n = 6 Field lines Ion guiding center punctures n = 5
Ion guiding center n = 5 n = 6 Field lines Jump across n = 5 separatrix
Ion guiding center n = 6 Field lines n = 6
Ion guiding center n = 6 Field lines Ion becomes stochastic
Ion guiding center n = 6 Field lines
Sharp transition from good connement to stochasticity As fast ions slow down their trajectories approach the eld lines. Overlapping of the ion islands triggers the stochasticity of the ion orbits. Transition threshold ρ ci /a 0.05.
Sharp transition from good connement to stochasticity As fast ions slow down their trajectories approach of eld lines. Overlapping of the ion islands triggers the stochasticity of the ion orbits. Transition threshold ρ ci /a 0.05. Stochasticity can also be triggered by increase in fluctuation amplitude. Amplitude increases x3 during reconnection events in MST.
Counter-Injection shows increased prompt losses... Neutron Signal Co-Injection Counter-Injection
...and degraded connement Neutron Signal Co-Injection Counter-Injection Normalized Neutron Signal τ= τ = 20ms τ = 4ms
Ion orbit stochasticity increases for counter-injection Changing direction of B θ lowers q IGC instead of raising it. Safety factor (counter-injection) Ion start radius n=8 IGC start n=11
Conclusions Fast ion connement measured for the rst time in RFP. The fast ion slowing down agrees with classical Coulomb collisions with plasma electrons and ions. The connement is much better than it could be expected from a simple model of particles following stochastic eld lines. The difference is attributed to different resonance properties of magnetic eld and ions due to ion drifts. The connement is expected to be even better in improved connement plasma with lower fluctuations.
Thoughts after conclusions Positive spin on the reactor concept of RFP. Magnetic eld stochasticity may be not detrimental for the connement of fast particles. Threshold transition to stochastic transport may be used for the ash removal.
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