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Published byVincent Hart Modified over 8 years ago
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A.Yu. Chirkov1), S.V. Ryzhkov1), P.A. Bagryansky2), A.V. Anikeev2)
PLASMA KINETICS MODELS FOR FUSION SYSTEMS BASED ON THE AXIALLY-SYMMETRIC MIRROR DEVICES A.Yu. Chirkov1), S.V. Ryzhkov1), P.A. Bagryansky2), A.V. Anikeev2) 1) Bauman Moscow State Technical University, Moscow, Russia 2) Budker Institute of Nuclear Physics, Novosibirsk, Russia
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Neutron generator concept:
Simple mirror geometry with long central solenoid Injection of energetic neutrals Neutron generator concept: T ~ keV, n ~ 1019 m–3, a ~ 1 m, L ~ 10 m, B ~ 1..2 T in center solenoid, ~ 20 T in mirrors, fast particle energy ~ keV, Pn Pinj
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The power balance scheme
Local balance Plasma amplification factor
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Radiation losses Electron – ion bremsstrahlung mec2 = 511 keV
Electron energy losses during slowing down on ions 1 10 100 103 104 105 1.1 1.2 1.3 1.4 1.5 1.6 2 3 Te, eV g ––––– fit – - – - Elwert Gould CE = Pei – correction to the Born approximation – for Te ~ 1 keV [Gould] Integral Gaunt factor: Approximation taking into account Gaunt factor for low temperatures: Gaunt factors for low temperatures. Approximations of B: 1 – formula corresponds g 1 at Te 0; 2 – g gElwert at Te 0; 3 – by Gould
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Approximations of numerical results
Electron – electron bremsstrahlung CF = (5/9)(44–32) 8 CE = Approximations of numerical results
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Synchrotron radiation losses
1 Ps/Ps0 10–3 Te, keV 10–2 . –––– Trubnikov – – – Trubnikov + relativistic corr. Tamor, Te < 100 keV – - – - Tamor, Te = 100–1000 keV – - - – Kukushkin, et al. Emission in unity volume of the plasma: Losses from plasma volume (Trubnikov): Output factor: – Trubnikov Output factors at a = 2 m, Rw = 0.7, Bext = 7 T, 0 = 0.1 (upper curves) and 0 = 0.5 (down) – relativistic correction [Tamor] 0.2 0.4 0.6 0.8 1 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Trrel 0 2 3 4 1 – Te = Ti = 30 keV 2 – 50 keV 3 – 70 keV 4 – 90 keV a = 2 m, Rw = 0.7, Bext = 7 T Generalized Trubnikov’s formula for non-uniform plasma [Kukushkin et al., 2008]: Output factor vs 0 at a = 2 m, Rw = 0.7, Bext = 7 T, Te = Ti = 30 keV (1), 50 (2), 70 (3), and 90 keV (4)
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Fast particle kinetics
b Proton slow-down rate (a) and cross section (b) for interaction with electrons ( ), deuterium ions (–––––) and helium-3 ions (– - – - –): 1, 2 – Coulomb collisions, 3 – nuclear elastic scattering D–T reaction and slow-down cross sections ratio for tritium ions in the deuterium plasma with Ti = Te = T
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Optimal parameters: T 10 keV, Einj 100 keV, Pn Pinj ~ 4 MW/m3
Some estimations High-energy approximation: MW/m3 m3/s keV keV keV Optimal parameters: T 10 keV, Einj 100 keV, Pn Pinj ~ 4 MW/m3
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The Fokker – Planck equation
Boundary conditions: In the loss region Quasi isotropic velocity distribution function:
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Numerical scheme Scales and dimensionless variables:
Dimensionless equation (symbols “~” are not shown):
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Finite difference equations:
Numerical scheme Greed: Finite difference equations: Matrix form:
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Solution:
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Examples of numerical calculations
Velocity distribution function of tritium ions and its contours at time moments after injection swich on t = 0.1s (а), 0.3s (b) и 10s (c). Deuterium density nD = 3.31019 м–3, energy of injected particles 250 keV, injection angle 455, injection power 2 MW/m3, Ti = Te = 20 keV, = 10 keV, slow-down time s = 4.5 s, transversal loss time = s
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Relative pressure and density of alphas in D–T plasma (D:T = 1:1):
Role of particles in D–T fusion mirror systems 5 1 2 . 4 8 T, keV 3 n /n0 p /p0 5 1 2 . 6 4 8 3 T, keV /s WL /W0 Relative pressure and density of alphas in D–T plasma (D:T = 1:1): –––––– isotropic plasma (no loss cone) – – – – mirror plasma with loss cone n0 = nD + nT = 2nD p0 = pD = pT Energy losses (WL) due to the scattering into the loss cone and corresponding energy loss time () of alphas in D–T mirror plasma W0 is total initial energy of alphas (3.5 MeV/particle) s is slowdown time
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Parameters of mirror fusion systems:
Neutron generator and reactors with D–T and D–3He fuels Parameter Neutron generator regimes Tandem mirror reactors Ver. # 1 Ver. # 2 Ver. # 3 Ver. # 4 D–T fuel D–3He fuel Plasma radius a, m 1 Plasma length L, m 10 44 Magnetic field of the central solenoid B0, T 1.5 2 3.3 5.4 Magnetic field in plugs (mirrors) Bm, T 11 14 14.8 Averaged 0.5 0.2 0.7 Deuterium density nD, 1020 m–3 0.26 0.22 0.21 0.415 0.82 1.35 Ion temperature Ti, keV 22 15 65 Electron temperature Te, keV 10.5 8.5 18 19 Ion electrostatic barrier , keV 16.5 33 60 260 Injection power Pinj, MW 74 55 – ECRH power PRH, MW Neutron power Pn, MW 24 30 43 59 Plasma amplification factor Qpl = Pfus/(Pinj + PRH) 0.38 0.9 1.34 Total neutron output N, 1018 neutrons/s 13 26.5 Neutron energy flux out of plasma Jn, MW/m2 0.4 0.04 Heat flux out of plasma JH, MW/m2 1.2 1.8 2.0 2.4 0.94
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Thank you!
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