Dr. Martin Droba Darmstadt

Transcription

1 Numerical Models for NNP Confinement Dr. Martin Droba Darmstadt

2 Contents l NNP (Non-neutral Plasma) l Motivation l High current ring l Codes l Diocotron Instabillity and Diagnostic l Toroidal segments and injection experiment 2

3 Neutral Plasma Number of particles in Debye sphere nλ D3 >> 1 Debye length smaller than size of plasma λ D < L Observed time scale longer than T > 2π/ω p Neutrality -> +=- (quasineutrality) 3

4 Non-neutral neutral Plasma Number of particles in Debye sphere nλ D3 >> 1 Debye length smaller than size of plasma λ D < L Observed time scale longer than T > 2π/ω p Neutrality -> +=-(quasineutrality) 4

5 Motivation l High current (density) beams Transport? Accelaration? Accumulation? l Space charge compensation l Interaction with Non-neutral plasma (NNP) l Using of guiding magnetic fields Drifts l High current beam projects FRANZ (Frankfurt neutron generator) High current storage ring 5

6 Motivation beam Space charge compensation electron cloud l Influence of external fields? 6

7 Solenoid -Momentum change -Rotation -Momentum change r r 2 ( p qa) H = + qφ 2m r r r pstart = psol + qa, angular momentum and energy conservation r B0 r A for hard edge solenoid = Aϕ = 2 7

8 Toroidal segment l Effects - density variation electric hoop forces - mirror charges - centripetal force - change of momentum 8

9 Toroidal transport - Drifts R B toroidal segments l Role of compensation electrons in mirror-like configuration l Drifts ExB, centripetal force, grad B l Different densities n e, n p and focusing properties Brillouin flow limit 9

10 Magnetic connection of segments l Magnetic Momentum µ = mv 2B 2 Higher Orders Conservation when field change small For example B -Variation 0.3T in 300mm => r db dt mv r r r < µ >= µ 0(1 b b) qb d r ( = + v b ) dt t << Ω r r r 0.3T qb = ( + v b ) B ~ v = << Ω B = B = t 0.3m m

11 Figure-8 Storage Ring l R ~ 1m l r ~ 0.2m l L~10m l 22 toroidal segments l h ~ 1m l B ~ 5T l I ~ 10A 11

12 Reactivity of different fusion processes N.Rostoker

13 Fusion reaction in the ring fusion reaction 11 B+p -> 3α (8.7MeV); fusion cross section σ max ~ m 2 Reactivity of 150 kev proton beam in dependence from beam temperature 13

14 ω c [s n B [m -3 ] Beam radius a[m] 0.01 Debye length [m] ExB rotation time [s] Ultra high vacuum (n ~ m -3 ~ hpa) Collision time τ c [s] Confinement time in toroidal magnetic field (Crooks 1994) Confinement time on magnetic surface (Pedersen 2003) 12.5 τ τ c (R/λ D ) 2 τ τ c (a/λ D ) 4 14

15 Codes l Field mapping Biot-Savart solver (Predictor-Corrector method, Field-line integration 1D information) l Frequency decomposition FFT (for every surface 1D => 2D) l Reverse mesh design in new coordinates ψ<0,1>, θ<0,2π>, ξ<0,2π> l Poisson equation l Guiding center drift motion Parallel cluster of CSC (Centre for Scientific Computing) 15

16 Cylindrical coordinates r, ϕ, z Toroidal coordinates r, θ, ξ Magnetic coordinates (Clebsch, Boozer...) ψ, θ, ξ ψ, α, χ 16

17 Frequency decomposition FFT (for every surface 1D => 2D) χ = Bdl 17

18 Guiding centre equations α φ 1 = µ + dt ψ e d 2 eb ρ m B ψ ρ = mv eb ψ = dt φ 1 eb + µ + ρ α e m d 2 dχ dt 2 eb mc ρ = B α χ = Bdl ρ φ 1 = µ + dt χ e d 2 eb ρ mc B χ 18

19 Poisson Poisson equation equation ),, ( ξ θ ψ = + + = q q z q y q x h i i i i Orthogonal basis 19 ),, ( ξ θ ψ = q + + = ξ φ ξ θ φ θ ψ φ ψ φ h h h h h h h h h h h h On axis integral Gauss law Numerical iteration method, parallel implementation

20 Test example Potential distribution example for circulating test beam at Cut through magnetic structure along ξ, θ plane ξ=ξ 1 video 20

21 Gabor-Lens 21

22 Measurement of n,t profiles Auswertung Spektrometer Helmholtzspulen Faraday Cup Auswertung U ~ 5500V B ~ 0.013T p ~ 8E-5 mbar Optical measurements CCD CCD-Kamera Impulsspektrometer Rest gas ion detection energy spectrum Fenster Turbopumpe Diocotron instabillity ExB surface wave n ~ m -3 Typicall time scale ~ 1µs 22

23 Diocotron Instabillity 23

24 Content video 24

25 Toroidal segments Parameters Toroidal magnetic field on axis = 0.6 T Major Radius = 1300 mm Minor Radius = 100 mm Bending angle: 30, Axis length: 770 mm B-Feld max: 0,6 T Current source: 30 V, 400 A Water cooling: 6 bar, 20 C Brillouin-Flow-Limit: 9,5E14 1/m 3 Calculated FxB drift in 1 Segment: ca. 18 mm Injection Beam Energy = 20keV max 25

26 First transport experiments 26

27 First comparison with experimental data Simulated beam emittance H +,H 3 + Measured beam emittance 27

28 Injection Experiment v y[m] / v Proposed injection experiment x[m] velocity ratio in Toroid-2 according to auxiliary coil entrance 28

29 Simulation Injected 10keV, H+ 0.6T help 0.2T Influnce on ring beam 29

30 Summary space charge compensation in torodial beam transport investigation of beam drift effects investigation of beam instabillities experimental study of beam injection evaluation of numerical simulation with experimental results 30

31 NNP Group M. Droba Ring Design N. Joshi Injection Experiment O. Meusel Gabor-Plasma-Lens K. Schulte Diagnostic of NNP L.P.Chau Bunch Compressor C.Wiesner Chopper System 31