Tokamak

Choose Tokamaks

Major radius

miner radius

BT

Line averaged electron density

Averaged electron Temperature

Plasma current

Gyrotron frequency

Neutral beam energy

Electron Temperature `T_e`

\( KT=E\)

Debye length `lambda_D`

\(\lambda_D=\sqrt{\frac{\epsilon_0 KT_e}{n_e e^2}}\)

electrons in a debye sphere 

\(n_e \lambda_D^3\)

average distance 

\(d=n^{-1/3}\)

\(kT/E_{coulomb}\) 

\(kT/E_{coulomb}=4\pi(n_e\lambda_D^3)^{2/3}\)

magnetic pressure 

\(p_B=\frac{B^2}{2\mu_0}\)

plasma pressure 

\(p=nKT\)

Aspect ratio 

\(ratio=R/a \)

plasma frequency at centre 

\(f_{pe}=\frac{1}{2\pi}\sqrt{\frac{n_e e^2}{\epsilon_0 m}}\)

Electron cyclotron frequency at centre 

\(f_{ce}=\frac{e Bt}{m}\frac{1}{2\pi}\)

O-mode density limit 

\( f_{pe}(n)=f_{ce}\,\,\, n\approx Bt^2 \times 10^{19}\)

Centre X2 mode density limit 

\(\displaylines{\frac{X}{Y}=\frac{\omega_{pe}^2(n)}{\omega^2}\frac{\omega^2}{\omega_{ce}^2}=\frac{1}{2}\times\frac{4}{1}=2\,\,\, \\ n \approx 2Bt^2 \times 10^{19}}\)

D neutral beam damping length `bar lambda`

\(\bar \lambda=5.5\times 10^{17}(E_b(keV)/A_b)/n_e(/m^3) \)

Greenwald density  

\(n_G(10^{20}/m^3)=\frac{I_p(MA)}{\pi a^2} \)

first harmonic resonance position  

\(RB_T=(R+\rho_1a)\frac{f_g}{28} \)

2nd harmonic resonance position 

\(RB_T=(R+\rho_2a)\frac{f_g}{28\times 2} \)

O mode cutoff local density 

\( n_o^2=1-\frac{f_{pe}^2}{f_g^2}>0 \,\,\,f_{pe}=8.98\sqrt{n}\)

X2 density limit 

\(X=\frac{\omega_{pe}^2}{\omega^2}=\frac{1}{2}\,\,\, Y=\frac{\omega_{ce}^2}{\omega^2}=\frac{1}{4}\)

O mode cutoff position 

\(\displaylines{(n_{e0}-n_{ea})(1-r^2)+n_{ea}=n_{cutoff}\\ n_{e0}=1.5 \bar n_e\,\,\, n_{ea}=n_{e0}/5}\)

Toroidal field profile 

\( R B_T=(R+\rho a)B(\rho)\)

\(f_{cH}\) 

\(f_{cH}=2f_{cD}=\frac{e B}{m_i}\frac{1}{2\pi}\)

\(f_{cHe_3}\) 

\(f_{cHe_3}=2f_{cT}=\frac{2 e B}{3 m_i}\frac{1}{2\pi}\)