Experimental evaluation of nonlinear collision effect on the beam slowing-down process

Transcription

1 P-2 Experimental evaluation of nonlinear collision effect on the beam slowing-down process H. Nuga R. Seki,2 S. Kamio M. Osakabe,2 M. Yokoyama,2 M. Isobe,2 K. Ogawa,2 National Institute for Fusion Science, Toki, Japan 2 SOKENDAI (The Graduate University for Advanced Studies), Toki, Japan H. Nuga (NIFS) Sep./27 / 5

2 Summary Summary Aims of this research Results To develop a Fokker-Planck (F-P) simulation code for the analysis of the behavior of Energetic Particles (EPs) in fusion plasmas. To validate our F-P code, especially beam-beam (b-b) collision effect, the neutron emission rate on LHD is analyzed. The effect of b-b collision appears clearly in LHD experiments. The effect is estimated by the neutron emission rate. Our F-P code can describe the b-b collision effect. The simulation results have same tendency to experiments. The absolute value of the simulated neutron emission rate is over estimated. Lack of fast ion loss mechanisms. Too simple assumptions. H. Nuga (NIFS) Sep./27 2 / 5

3 intro Introduction Background To analyze the behavior of beam ions, implementation of a Fokker-Planck code, TASK/FP, in integrated code TASK3D-a is ongoing. Experiment group requires codes enable to estimate followings: Beam heating power to electron and ions. Neutron emission rate from DD reaction. r and v distribution of beam ions. On LHD, GNET code (Monte Carlo) has been used for analyses. This code is accurate but heavy. A code which obtains the computational performance in exchange for the loss of accuracy is required. F-P code is suitable. F-P codes require less CPU than particle codes. Easy to calculate time evolution of f. Difficult to include orbit width effect. The progress of the implementation and some analysis results using TASK/FP are presented. H. Nuga (NIFS) Sep./27 3 / 5

4 intro Introduction Motivation We focus on the contribution of b-b collision to EPs. Two EPs, which have similar velocity, may interact each other through b-b collision effect. This effect may deform f of EP. There is a possibility b-b collision influences to the beam confinement. Ex.) May distorted f of α particle by NBI affect AE in ITER? Nonlinear collision model[] adopted in our code can take the effect into account. To validate our code, a series of experiments, which use tangential H and D NBs, were held. B.J. Braams, Phys. Fluid B,, 355, (989). H. Nuga (NIFS) Sep./27 4 / 5

5 intro Introduction Process of F-P analysis In our F-P analysis, FIT3D[,2] and TASK/FP[3,4] are combined. FIT3D calculates birth fbeam abs (p, θ, ρ) from E beam, P port, and plasma beam parameters. TASK/FP calculates time evolution of f beam (p, θ, ρ) using f abs beam as a source term. Code name Input Output Role FIT3D (HFREYA) E beam, P port beam Birth profile Calculate beam ionization FIT3D (MCNBI) Birth profile P abs beam abs (p, θ, ρ) Calculate prompt loss TASK/FP n e, T e, T i, fbeam abs beam(p, θ, ρ, t) Calculate evolution of f beam S. Murakami, et al, Fusion Technology, 27, P. Vincenzi, et al, Plasma Phys. Control. Fusion, 58, 2, 258, H. Nuga, A. Fukuyama, Progress in Nuclear Science and Technology, 2, 78, 2. 4 H. Nuga, et al, Phys. Plasmas, 23, 6256, 26. H. Nuga (NIFS) Sep./27 5 / 5

6 intro Introduction Simulation Code: TASK/FP TASK/FP is a Fokker-Planck code to calculate the time evolution of momentum distribution function f in 3 dimension : (p, θ, ρ). Fokker-Planck equation in (p, θ, ρ) coordinate f s t = p S + H, H = S NB + L CX ( f ) + S n f ( f ) + L sink ( f ) + R( f ) Note: H includes beam source, charge exchange loss, fusion reaction source and loss, artificial loss, and radial diffusion terms. In the present, the radial diffusion term is not used. H. Nuga (NIFS) Sep./27 6 / 5

7 intro Introduction Code extension for experimental analysis Although TASK/FP is developed as a prediction code originally, to use for experimental analysis, it is extended as below. Momentum distribution function is divided into two components: bulk f and non-thermal f b, namely f = f + f b. Bulk component f is a Maxwellian with measured n and T. Bulk component f is updated by Maxwellian in each time step. Evolution of f b is calculated by using F-P eq. f b t = S + S NB + L CX ( f ) + S n f ( f ) + L sink ( f ) + R( f ) S NB is obtained from FIT3D. To conserve the density in the bulk region, f b has a sink term in < p < 3p th, L sink. H. Nuga (NIFS) Sep./27 7 / 5

8 Experiment for the validation of the non-linear collision effect F-P code can describe the b-b collision. To validate the effect, the following experiment was planned. D distribution function[*.e-4] D beam E=8keV co direction H beam 8keV ctr direction H beam 8keV t=ms after NB#3 off w NB#2 (balance injection) no background NB w NB# (both co-injection) energy in beam direction [kev] Preliminary simulation Focus on the slowing down process of the tangential D beam in D plasmas with tangential H beam. If D and H beam have a same direction, D beam ions are accelerated by H beam because H beam is faster than D beam. If they have different direction, D beam ions are not affected by H beam owing to the large relative velocity. H. Nuga (NIFS) Sep./27 8 / 5

9 Preliminary pre-experiment estimation The contribution of beam-beam collision can be estimated through the measurement of the neutron emission rate by D-D reaction. Focus on the decay time of neutron emission rate after D beam offs. beam energy[kev] fusion reaction rate background co- or ctr H beam short pulse D beam time[sec].6e-6.2e-6 8e-7 4e-7 beam wave form n=5e9 n=3e9 n=2e9 n=e9 n=.5e9 co beam time [sec] Evolutions of neutron emission rate It is expected that if D and H beam have a same direction, the decay time becomes longer due to the beam-beam collision. :decay time of neutron rate [sec] τd preliminary simulation result # and #3 (both co-injection) #2 and #3 (balance injection). BG co beam extendsτd τs :beam slowing down time[sec] Decay time with respect to slowing down time. H. Nuga (NIFS) Sep./27 9 / 5

10 ne[e9/m 3 ] Experiment on LHD NB#3: D co Te 6 Beam Energy[keV] Te [kev] Neutron counts [e4/s] NB#: H co- NB#2: H ctr time [sec] Example of waveform (SN37352) NB: H beam E 8keV, P port 5MW NB2: H beam E 6keV, P port 3.5MW NB3: D beam E 4keV, P port 2MW ne 3 2 (NB#2:H) E~6keV (NB#3:D) E~4keV NB injection system on LHD N-NBI (NB#: H) E~8keV Co- or ctr-direction H beam is overlapped on D beam. D beam offs at t = 4.8 sec. The decay time of neutron emission rate is investigated. H. Nuga (NIFS) Sep./27 / 5

11 Results of the decay time τ [sec] D.2. both cobalance no BG. τ [sec].2.3 s Results of decay time with respect to slowing down time. τ s τse e ln E 3/2 E 3/2 + E 3/2 C + E 3/2 C, Co-direction H beam tends to extend the decay time rather than balance-direction H beam. The differences appear clearly in long τ s region owing to the weak collisional friction. These results support that of the pre-experiment simulation. where τ se is the beam slowing down time, E C is the critical energy, E = 4 kev, and E = 5 kev satisfies: σv cx (E )/ σv cx (E ) τ cx (E )/τ cx (E ) = /e H. Nuga (NIFS) Sep./27 / 5

12 Fokker-Planck analysis using experiment data Assumptions T e = T i, n e = n i, n D /(n H + n D ) =.9 n i = n bulk i + n beam i Neutral gas profile is fixed. n n () = 4 m 3, n n () = 6 m 3 Radial transport of fast ions is ignored. Trapped particle effect is omitted (tangential beam). Contributions of fusion born H and T ions are neglected. 2 t=4.8 s 2 t=4.9 s both co-.2 balance no BG 6 6 τ D [sec] t=5. s t=5. s 6 2 SN τ [sec].2.3 s (SN37352 ρ = ) The relaxation of D beam distribution can be obtained in 2D momentum space. Distribution function of H ion is also calculated. H. Nuga (NIFS) Sep./27 2 / 5

13 Simulation of neutron emission rate (both co-injection) τ D [sec] 4 neutron counts [ /s] 4 neutron counts [ /s] both cobalance no BG SN37352 measurement short τs SN37346 SN37359 SN τ [sec].2.3 s simulation SN time [sec] measurement long τs simulation SN time [sec] R = f D (v a ) f D (v b )du a du b D-D reaction is calculated by double integration of f D obtained by F-P code. F-P simulation over estimates the neutron emission rate. The simulated decay time is longer than that of measured. Lack of fast ion loss mechanism. Typical time constants SN τ exp D [sec] τsim D τ s (ρ = ) τ s () CX loss time (τ cx () = 3.8sec, τ cx () =.69sec) is sufficiently longer than the slowing down time in the whole plasma. H. Nuga (NIFS) Sep./27 3 / 5

14 Simulation of neutron emission rate (balance injection) 4 neutron counts [ /s] 4 neutron counts [ /s] measurement short τs simulation SN time [sec] measurement long τs simulation SN time [sec] both cobalance no BG Simulation result of short τ s case has a good agreement. The value of the decay time is not matched especially in long τ s region. The extention of the decay time due to b-b collision also appears in this simulation. Typical time constants SN τ exp D [sec] τsim D τ s (ρ = ) τ s () τ D [sec].2.. τ.2 s [sec].3 It can be guessed fast ion loss plays a important role in long τ s region. τ exp + + τ D s τ cx τ EP L H. Nuga (NIFS) Sep./27 4 / 5

15 Conclusion To analyze the behavior of EPs on LHD, F-P code have been developed. To validate the code, especially b-b collision effect, a series of experiment, which focus on the beam slowing down process, was held. The b-b collision effect is estimated by the neutron emission rate. In LHD experiments, the effect of b-b collision appears clearly. F-P simulation results have same tendency. the neutron emission rate is over estimated owing to the lack of loss mechanism. H. Nuga (NIFS) Sep./27 5 / 5