Notes on fusion reactions and power balance of a...
Transcript of Notes on fusion reactions and power balance of a...
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Chapter 5
Notes on fusion reactionsand 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.
SA, 3/2017
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Exoenergetic reactions: fusion and fission reactions
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Exoenergetic reactions = energy releasing reactions
1 + 2 = > 3 + 4 + ... + 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
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D + 3He --> α (3.67 MeV) + p (14.7 MeV)
a few fusion reactions
the easiest
deuterium cycle
a dream
in the Sun(first of a chain)
p + p --> D + e+ + ν
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Fusion reaction cross sections
pp cross-section extremely small: 3 x 10-26 barn at energy of 10 keV
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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
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Thermonuclear reaction rate
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where• n1 = number density of nuclei “1”• n2 = number density of nuclei “2”• δ12 = Kronecker δ • = 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
depends on temperature only (for a given reaction)
Volumetric reaction rate for the reaction between nuclei of species “1” and “2” = number of reactions per unit volume and unit time
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Maxwellian averaged reactivities
D + T => α + n + 17.6 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
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Even for DT, temperature > 5 keV required for thermonuclear plasma self-sustainement
A (simplified) necessary condition for DT plasma self-sustainement:
D + T => α + n + 17.6 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
at 4.2 keV fusion alpha particle power exceeds bremsstrahlung power
11ideal ignition temperature
€
nDnT < sv >QDT5
> neniCb T
< sv > QDT20
> Cb T
(assuming equimolar pure DT plasma)
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Steady-state plasma power balance
power balance (per unit volume):
• losses: • bremsstrahlung ∝ n2 T1/2 , 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 ∝ n2 • auxiliary heating: (fusion power)/Q
Q: energy multiplication [1/Q: fraction of re-cycled fusion energy]Q = ∞ : ignition (self-sustainment of plasma temperature)
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Lawson criterion
T = 10 - 20 keVnτ ≥ 2 x 1020 m-3 s
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Triple product n τ T
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Magnetic and inertial plasma confinement
• magnetic confinement fusion (MCF):
quasi-steady state fusion power release from low density plasma (1020-1021 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/cs, where R is a characteristic dimension (e.g. radius of a plasma sphere, and cs is the sound speed).
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Magnetically confined thermonuclear fusion plasma
• T > 10 keV
• plasma pressure (p = 2nkBT) contained by magnetic field pressure B2/2µ0;
in practice p = 2 n kB T = β B2/2µ0 with β ≤ 0.1
⇒ for T = 5 tesla, n ≤ few units x 1020 m-3
⇒ energy confinement times τΕ ≈ 1 - 5 s
T = 10 - 20 keVn ≈ 1014 cm-3τ ≈ 1 - 5 s
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