Notes on fusion reactions and power balance of a thermonuclear plasma!

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1 SA, 3/2017 Chapter 5 Notes on fusion reactions and power balance of a thermonuclear plasma! Stefano Atzeni See S. Atzeni and J. Meyer-ter-Vehn, The Physics of Inertial Fusion, Oxford University Press (2004, 2009), Chapter 1 and Chapter 2.

2 Exoenergetic reactions: fusion and fission reactions Exoenergetic reactions = energy releasing reactions = > Q, with energy Q > 0 For Einstein mass-energy relation, Q > 0 if the total mass of the reaction products is smaller than the mass of the reactants Equivalently, if we consider the nuclear binding energies B: Exoenergetic reactions < = => average binding energy per nucleon increases 2

3 a few fusion reactions the easiest deuterium cycle D + 3 He --> α (3.67 MeV) + p (14.7 MeV) a dream in the Sun (first of a chain) p + p --> D + e + + ν

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6 Fusion reaction cross sections pp cross-section extremely small: 3 x barn at energy of 10 kev 6

7 For energy production: thermonuclear fusion beam-target reactions (between an accelerated nucleus and target at rest) or! beam-beam reactions cannot be used for net energy production, because scattering and slowing down dominate over fusion (accelerated nuclei are slowed down before they fuse; the energy they lose cannot be recovered) energy production requires a hot plasma => thermonuclear fusion! In a hot plasma fast nuclei (ions) collide with other nuclei and electrons; the energy lost by one particle is gained by another particle within the same thermal distribution

8 Thermonuclear reaction rate Volumetric reaction rate for the reaction between nuclei of species 1 and 2 = number of reactions per unit volume and unit time where n 1 = number density of nuclei 1 n 2 = number density of nuclei 2 δ 12 = Kronecker δ <σv> = Mawellian averaged reactivity Maxwellian averaged reactivity: product of the cross section σ(v) times the relative velocity of the reacting nuclei, averaged over the Maxwellian velotityy distribution <σv> depends on temperature only (for a given reaction) 8

9 Maxwellian averaged reactivities D + T => α + n MeV has by far the largest reactivity DT reactivity is maximum at T = 64 kev At T < 60 kev is at least 10 times larger than the reactivity of any other reaction 9

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11 Even for DT, temperature > 5 kev required for thermonuclear plasma self-sustainement A (simplified) necessary condition for DT plasma self-sustainement: at 4.2 kev fusion alpha particle power exceeds bremsstrahlung power D + T => α + n MeV 14.1 MeV neutrons: leave the plasma; 3.5 MeV α-particles: can be slowed in the plasma. Plasma emits bremsstrahlung Plasma temperature self-sustainement: fusion α-particle power Bremsstrahlung n D n T < sv > Q DT 5 > n e n i C b T < sv > Q DT 20 > C b T (assuming equimolar pure DT plasma) ideal ignition temperature 11

12 Steady-state plasma power balance power balance (per unit volume): losses: bremsstrahlung n 2 T 1/2, where n is the electron density other, characterized by an energy confinement time τ: 3 n T/τ (assuming equal densities and temperatures for electron and ions) input: fusion-α power = (1/5) fusion power n 2 <σv> auxiliary heating: (fusion power)/q Q: energy multiplication [1/Q: fraction of re-cycled fusion energy] Q = : ignition (self-sustainment of plasma temperature) 12

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14 Lawson criterion T = kev nτ 2 x m -3 s

15 Triple product n τ T 15

16 Magnetic and inertial plasma confinement magnetic confinement fusion (MCF): quasi-steady state fusion power release from low density plasma ( m -3 ), in quasi steady-state, contained by appropriately shaped magnetic fields inertial confinement fusion (ICF): explosive fusion energy release from a strongly compressed plasma; theplasma pressure cannot be sustained by any means. Therefore the compressed plasma is confined by its inertia only, and remains compressed for a time τ R/c s, where R is a characteristic dimension (e.g. radius of a plasma sphere, and c s is the sound speed). 16

17 Magnetically confined thermonuclear fusion plasma T > 10 kev plasma pressure (p = 2nk B T) contained by magnetic field pressure B 2 /2µ 0 ; in practice p = 2 n k B T = β B 2 /2µ 0 with β 0.1 for T = 5 tesla, n few units x m -3 energy confinement times τ Ε 1-5 s T = kev n cm -3 τ 1-5 s

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ICF ignition and the Lawson criterion

ICF ignition and the Lawson criterion Riccardo Betti Fusion Science Center Laboratory for Laser Energetics, University of Rochester Seminar Massachusetts Institute of Technology, January 0, 010, Cambridge