Question

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euestions The Debye length, AD, is given by e n potential in a plasma. g the spatial variation of the electric 14 Calculate the temperature of a Tokamak plasma of density 3 x 1019 m3 that has a Debye 121 In a plasma entirely consisting of electrons and protons confined within an b) Length of 0.18 mm. c) inhomogeneous magnetic trap, the minimum and maximum magnetic fields are 0.30 T and 2.7 T respectively. Expressing your answers in Hz, calculate (i) The maximum cyclotron frequency of any charged particle anywhere within this trap. 121 (i) The minimum cyclotron frequency of any charged particle anywhere within this trap. [You may assume that the plasma is non-relativistic.]

Answer 1

Debye length lambda_D = squareroot epsilon_0 k_B T_c/e^2 n_e a) Electric potential is a plasma 'phi' phi = phi_0 e^-lambda_D x At x = lambda_D, phi = phi_0/e So, potential decrease rapidly as we more from x = 0 to lambda_D b) For a Tokamak plasma, n_c = plasma density = 3 times 10^19 m^-3 lambda_D = 0.18 times 10^-3 m Since lambda^2_D = epsilon_0 k_B T_c/n_e e^2 implies T_e = lambda^2_D n_e e^2/epsilon_0 k_B Here, e = 1.6 times 10^-19 c, epsilon_0 = 8.85 times 10^-12 c^2 N^-1 m^-2 k_B = 1.38 times 10^-23 J/k Therefore T_e = 0.18 times 0.18 times 10^-16 times 3 times 10^19 times 1.6 times 1.6 times 10^-38/8.85 times 10^-12 times 1.38 times 10^-23 T_e = 2.0374 times 10^8 k rightarrow temperature of Tokamak plasma c) Max B = 2.7 T & Min B = 0.3 T (i) max. cyclotron frequency can be due to electrons and B = 2.7 T w = qB/m..
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