Assume that the 1-D density profile is -n(1-) T=T(1-9) n = (1 and the temperature profile...

 

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Assume that the 1-D density profile is -n(1-) T=T(1-9) n = ñ(1 and the temperature profile is where r is the radial coordinate variable and a is the minor radius of tokamak. Answer the following questions (a) The plasma volume averaged alpha power density can be written as 2 Sa a2 n² rdr Assume (ov) = C,T2 where C, is the reaction rate coefficient. Find S in terms of ñ, T, Ea, Cg. (b) The conduction transport term can be written as 2 ra (3nT Sx rdr %3D a2 TE where TE is the confinement time. If Tg is a constant, find Sg in terms of ñ, T,TE (c) When the radiation loss is ignorable, find the condition of the 0-D power balance for ignition using (a) and (b). Use C, = 10-18cm3/s/(keV)2 (d) Calculate the minimum confinement time TĘ for the condition (c) for ñ = 1020 m-3 and T = 15 keV. This problem is modified from Pb. 4.4. of the textbook [Freidberg], and the purpose is to check the 0-D power balance from the 1-D radial density and temperature profiles. Assume that the 1-D density profile is -n(1-) T=T(1-9) n = ñ(1 and the temperature profile is where r is the radial coordinate variable and a is the minor radius of tokamak. Answer the following questions (a) The plasma volume averaged alpha power density can be written as 2 Sa a2 n² rdr Assume (ov) = C,T2 where C, is the reaction rate coefficient. Find S in terms of ñ, T, Ea, Cg. (b) The conduction transport term can be written as 2 ra (3nT Sx rdr %3D a2 TE where TE is the confinement time. If Tg is a constant, find Sg in terms of ñ, T,TE (c) When the radiation loss is ignorable, find the condition of the 0-D power balance for ignition using (a) and (b). Use C, = 10-18cm3/s/(keV)2 (d) Calculate the minimum confinement time TĘ for the condition (c) for ñ = 1020 m-3 and T = 15 keV. This problem is modified from Pb. 4.4. of the textbook [Freidberg], and the purpose is to check the 0-D power balance from the 1-D radial density and temperature profiles.