Long-Range Collisions: Results and Open Ques5ons

Transcription

1 Long-Range Collisions: Results and Open Ques5ons C. Fred Driscoll UCSD Expts : M. Affolter, F. Anderegg, B. Beck, J. Fajans, K. Fine, E. Hollman, X.-P. Huang, A. Kabantsev, J. Kriesel Theory: D. Dubin, T. O'Neil, M. Glinsky, D.-Z. Jin Work supported by NSF/DoE Partnership grants PHY and DE-SC NNP-017

2 Classical and Long-Range Transport Coefficients cross-field par-cle diffusion Kinema-c shear viscosity Cross-field thermal diffusivity slowing rate D ν // λ = η nm χ = κ 3n ν c nvb b = e T classical 4 ρ < r c 3 π ν c r c ln ρ max 5 π ν c r c ln ρ max 16 9 π ν c r c ln ρ max b 4 3 π ν c ln ρ max ρ max = Min(r c,λ D long range ρ > r c D bounceaveraged for f b > S Longmire 1956 McWilliams 1987 π ν c r c ln λ D r c (Lifshitz&Pitaevskii Dubin 1997, Anderegg π f B Dubin 001 Anderegg 00 ln S ν c r c ln r δ ω p Ω c γ Longmire1956 Simon ν c λ D ln ω p γ (+ waves O Neil 1985, Dubin 1988, Driscoll π f B S ν c δ g(δ / r Dubin 1998 Kreisel 001 Braginskii ν c λ D (+ waves Rosenbluth 1976 Dubin 1998 Hollmann 000 NA Spitzer 196 Bowles 1994 π ν c 5.898ln Dubin 014 Affolter 016 NA d Max(b, r c λ + ln D Max(d, r c d 5 = b 3 v S = r ʹ ω E γ = Max(S,ν c δ = 4D / S f B = v / L ν //

3 Collision Rates : ν c (n, T ; B, ʹ ω ExB, f bou Short-Range Velocity-Scajering b < ρ < r c b = e / T = (1.44e-9 m T ev -1 r c = v / Ω = (1.0e-3 m T 0.5 B kg -1 ρ Δr ν * // = 8 15 π nvb ln r c b Dynamical Reduc5on of Short-Range Perp-to-Parallel Collisions when r c < b

4 Collision Rates : ν c (n, T ; B, ʹ ω ExB, f bou Short-Range Velocity-Scajering b < ρ < r c ρ Δr 3D Long-Range Dris-Kine5c r c < ρ < λ D v ExB E r c d λ D ρ ρ Fokker-Planck fluctua5on-collisions, & v-reflec5on -par5cle Boltzmann collisions, & v-reflec5on d 5 = b 3 v ν = (0.37e-3 m T1/5 n /5 7 // End Reflec5on : Par5cles collide N bou = f bou / (r ω' ExB 5mes before being separated by shear

5 Collision Rates : ν c (n, T ; B, ʹ ω ExB, f bou Short-Range Velocity-Scajering b < ρ < r c ρ Δr 3D Long-Range Dris-Kine5c r c < ρ < λ D r c d λ D ρ ρ D Long-Range, Point-Vortex, "z-bounce-averaged" Dris-only, E E r c < ρ < λ D ω ExB ω + "Collisions" do not separate vor5ces; ExB r Shear in ω ExB searates vor5ces v ExB

6 Classical and Long-Range Transport Coefficients cross-field par-cle diffusion Kinema-c shear viscosity Cross-field thermal diffusivity slowing rate D ν // λ = η nm χ = κ 3n ν c nvb classical 4 ρ < r c 3 π ν c r c ln ρ max 5 π ν c r c ln ρ max 16 9 π ν c r c ln ρ max b 4 3 π ν c ln ρ max ρ max = Min(r c,λ D long range ρ > r c D bounceaveraged for f b > S Longmire 1956 McWilliams 1987 π ν c r c ln λ D r c (Lifshitz&Pitaevskii Dubin 1997, Anderegg π f B Dubin 001 Anderegg 00 ln S ν c r c ln r δ ω p Ω c γ Longmire1956 Simon ν c λ D ln ω p γ (+ waves O Neil 1985, Dubin 1988, Driscoll π f B S ν c δ g(δ / r Dubin 1998 Kreisel 001 Braginskii ν c λ D (+ waves Rosenbluth 1976 Dubin 1998 Hollmann 000 NA Spitzer 196 Bowles 1994 π ν c 5.898ln Dubin 014 Affolter 016 NA d Max(b, r c λ + ln D Max(d, r c d 5 = b 3 v S = r ʹ ω E γ = Max(S,ν c δ = 4D / S f B = v / L ν //

7 Test Par5cle Diffusion n (10 6 cm n T T (ev Confined, steady-state Mg+ ion plasma v y (10 3 cm / sec v dia v tot ms n t / n r x (cm 6 s 15 s LIF "tagging" of ions at r=0.5cm, subsequent detec5on of n t (r,t

8 first ExB Dris calcula5on, using "Integra5on along Unperturbed Orbits" >> 3x too small α = 1 Anderegg, 1997

9 10 - cm sec Ê Á Ë n ln( l D /r c 10 cm 3 - ˆ -1 B 7 3 T D 3D IUO D 3D D clas "Velocity Caging" (v-reflec5ons} cause α = 3x more collisions Integra5on along Unperturbed Orbits >> no mul5ple collisions D T (ev Dubin, 1997

10 Mul5ple Axial Bounce Enhancement of Diffusion 10 3 D meas D 3D D 3D N b ª D D / D 3D D TM Mul5ple axial bounces increase D. Minimal shear approaches "D-Point-Vortex" limit of Taylor-McNamara N b f b S µ 1 L p S

11 Shear Viscosity : Non-uniform n(r and ωr(r relax to shear-free profile. Driscoll, 1988

12 Short Plasmas Short --> Long >> Viscosity is Enhanced by N bou correlated bounce-collisions Kriesel, 001

13 Cross-Field Thermal Diffusion : Independent of B Independent of n Hollman, 000 Kabantsev, NNP-017

14 Long-Range Collisional Slowing: enhanced at small T, small n, large B ν s = π nvb ln Λ ~ ~ ln Λ = Fokker-Planck Boltzmann λ ln D ln max[d,r c ] + 0 +/- -/- Velocity Caging Classical d 4 3 ln( min[r,λ ] c D max[b,r c ] + b lnl Dubin 014 Affolter, NNP H +, B=3T 10 6 r c < b p+ Density (cm -3 e lnλ 3D classical T HeVL lnl e -, B=3T r c < b lnλ3d classical T HeVL

15 Classical and Long-Range Transport Coefficients cross-field par-cle diffusion Kinema-c shear viscosity Cross-field thermal diffusivity slowing rate D ν // λ = η nm χ = κ 3n ν c nvb classical 4 ρ < r c 3 π ν c r c ln ρ max 5 π ν c r c ln ρ max 16 9 π ν c r c ln ρ max b 4 3 π ν c ln ρ max ρ max = Min(r c,λ D long range ρ > r c D bounceaveraged for f b > S Longmire 1956 McWilliams 1987 α π ν c r c ln λ D r c (Lifshitz&Pitaevskii Dubin 1997, Anderegg π Ν b f B Dubin 001 Anderegg 00 ln S ν c r c ln r δ ω p Ω c γ Longmire1956 Simon 1955 α 0.585ν c λ D ln ω p γ (+ waves O Neil 1985, Dubin 1988, Driscoll 1988 Ν b 16π f B S ν c δ g(δ / r Dubin 1998 Kreisel 001 Braginskii ν c λ D (+ waves Rosenbluth 1976 Dubin 1998 Hollmann 000 NA Spitzer 196 Bowles 1994 π ν c 5.898ln α Dubin 014 Affolter 016 NA d Max(b, r c λ + ln D Max(d, r c d 5 = b 3 v S = r ʹ ω E γ = Max(S,ν c δ = 4D / S f B = v / L ν //

16 Summary 1 Long-range collisions enhance cross-field par5cle diffusion by about 10x. About 1/3 of this enhancement is from the unusual "velocity caging" which results in mul5ple correlated collisions. Long-range shear viscosity and thermal diffusivity coefficients both scale as ν c λ D, making them independent of magne5c field. Thus, relaxa5on to the thermal equilibrium density profile and uniform temperature is strongly enhanced. 3 Individual par5cle slowing rates are substan5ally enhanced at low temperatures, again including "velocity caging". Theory has characterized the new fundamental length scale d : for ρ < d, collisions are -body and point-like; whereas for ρ > d, mul5ple weak collisions occur simultaneously. 4 In axially short plasmas, bouncing par5cles will have mul5ple correlated collisions, further enhancing diffusion and viscosity. The number of correlated collisions is imited by radial shear in the plasma rota5on.

17 Collision Rates : ν c (n, T ; B, ʹ ω ExB, f bou Short-Range Velocity-Scajering b < ρ < r c ρ Δr 3D Long-Range Dris-Kine5c r c < ρ < λ D r c d λ D ρ ρ D Long-Range, Point-Vortex, "z-bounce-averaged" Dris-only, E E r c < ρ < λ D ω ExB ω + "Collisions" do not separate vor5ces; ExB r Shear in ω ExB searates vor5ces v ExB