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Non-equilibrium ignition criterion for magnetized deuterium–tritium fuel

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Abstract

In this paper, non-equilibrium ignition conditions for magnetized cylindrical deuterium–tritium plasma in the presence of an axial magnetic field have been investigated. It is expected that temperature imbalance between ions and electrons as well as the axial magnetic field will relax the threshold of ignition conditions. Therefore, ignition conditions for this model are derived numerically involving the energy balance equation at the stagnation point. It has been derived using parametric space including electron and ion temperature (Te, Ti), areal density (ρR), and seed magnetic field-dependent free parameters of B/ρ, mB, and BR. For B/ρ < 106 G cm3 g−1, mB < 4 × 104 G cm g−1, and BR < 3 × 105 G cm, the minimum fuel areal density exceeds between ρR > 0.002 g cm−2, ρR > 0.25 g cm−2, and ρR > 0.02 g cm−2, respectively. The practical equilibrium conditions also addressed which is in good agreement with the corresponding one-temperature magnetized mode proposed in previous studies. Moreover, it has been shown that the typical criterion of BR ≥ (6.13–4.64) × 105 G cm would be expectable. It is also confirmed that the minimum product of areal density times fuel temperature in equilibrium model is located in the range of T = 6–8 keV for all these free parameters, depending on the magnitude of the magnetic field. This is the entry point for the non-equilibrium model consistent with equilibrium model.

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Abbreviations

ρ :

Mass density (g cm−3)

R ≡ R stag :

Cylinder radius at stagnation (cm)

n :

Number density (cm−3)

n e :

Electron number density (cm−3)

n i :

Ion number density (cm−3)

n D :

Deuteron density (cm−3)

n T :

Triton density (cm−3)

T e :

Electron temperature (keV)

T i :

Ion temperature (keV)

B :

Magnetic field (G)

ν 0 :

Birth velocity of alpha particle (cm s−1)

ω e :

Electron cyclotron frequency (s−1)

ω α :

Larmor frequency of alpha particle (s−1)

ω i :

Ion cyclotron frequency (s−1)

c :

Speed of light (cm s−1)

e :

Unit charge (statC)

m e :

Electron mass (g)

m i :

Ion mass (g)

m α :

Alpha mass (g)

Z :

Atomic number (-)

Z α :

Alpha atomic number (-)

E f :

Fusion energy (erg)

E α :

Alpha particle energy (erg)

E n :

Neutron energy (erg)

f α :

Fraction of alpha energy deposition (none)

l α :

Mean free path of alpha particle (cm)

r αL :

Larmor radius of alpha particle (cm)

\(\bar{R}\) :

Ratio of cylinder radius to mean free path of alpha particle (none)

b :

Ratio of cylinder radius to Larmor radius of alpha particle (none)

k B :

Boltzmann constant (erg keV−1)

W α :

Fusion power density (erg cm−3 s−1)

W α,DT :

DT fusion power density (erg cm−3 s−1)

<σv>DT :

DT averaged reactivity (cm3 s−1)

W br :

Bremsstrahlung power density (erg cm−3 s−1)

W hc :

Heat conduction power density loss (erg cm−3 s−1)

h :

Planck constant (erg s)

κ e :

Braginskii thermal conductivity for electrons (cm−1 s−1)

κ i :

Braginskii thermal conductivity for ions (cm−1 s−1)

τ :

Collision time (s)

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Guilan, P.O. Box 41335-1914, Rasht, Iran

    E. Ghorbanpour, A. Ghasemizad & S. Khoshbinfar

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Ghorbanpour, E., Ghasemizad, A. & Khoshbinfar, S. Non-equilibrium ignition criterion for magnetized deuterium–tritium fuel. NUCL SCI TECH 30, 67 (2019). https://doi.org/10.1007/s41365-019-0592-4

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