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ITER Neutral Beam Model | iternb()

  • iefrf/iefrffix = 5
Output Description
\mathtt{effnbss} Neutral beam current drive efficiency in \text{A/W}
\mathtt{fpion} Fraction of NB power given to ions
\mathtt{fshine} Shine-through fraction of the beam

This model calculates the current drive parameters for a neutral beam system, based on the 1990 ITER model.1

Firstly the beam access is checked for such that $$ \bigg(1+ \frac{1}{A}\bigg) > (R_{\text{tangential}}/R_0) $$

The beam path length to centre is calculated:

\underbrace{\mathtt{dpath}}_{\text{Path length to centre}} = R_0 \sqrt{\left(\left(1+\frac{1}{A}\right)^2-\mathtt{frbeam}^2\right)}

Beam stopping cross-section (\sigma_{\text{beam}}) is calculated using the sigbeam method described here :

Calculate number of electron decay lengths to centre

\tau_{\text{beam}} = \mathtt{dpath}\times n_e \sigma_{\text{beam}}

Shine-through fraction of beam: $$ f_{\text{shine}} = e^{(-2.0 \times \mathtt{dpath} \times n_e \sigma_{\text{beam}})} \ $$

Deuterium and tritium beam densities: $$ n_D = n_i * (1.0 - \mathtt{f_tritium_beam}) $$

n_T = n_i * \mathtt{f_tritium_beam}

Power split to ions / electrons is calculated via the the cfnbi method described here

Current drive efficiency | etanb()

This routine calculates the current drive efficiency of a neutral beam system, based on the 1990 ITER model. AEA FUS 251: A User's Guide to the PROCESS Systems Code ITER Physics Design Guidelines: 1989 IPDG89, N. A. Uckan et al, ITER Documentation Series No.10, IAEA/ITER/DS/10, IAEA, Vienna, 1990

Input Description
\mathtt{abeam}, m_{\text{u,ion}} Beam ion mass (\text{amu})
\mathtt{alphan} Density profile factor
\mathtt{alphat} Temperature profile factor
\mathtt{aspect}, A Aspect ratio
\mathtt{dene20}, n_{\text{e,20}} Volume averaged electron density (10^{20} \text{m}^{-3})
\mathtt{ebeam} Neutral beam energy (\text{keV})
\mathtt{rmajor}, R Plasma major radius (\text{m})
\mathtt{ten} Density weighted average electron temperature (\text{keV})
\mathtt{zeff}, Z_{\text{eff}} Plasma effective charge
Output Description
\mathtt{etanb} Neutral beam current drive efficiency in \text{A/W}
\mathtt{zbeam} = 1.0
\mathtt{bbd} = 1.0

Ratio of E_beam/E_crit

\mathtt{xjs} = \frac{\mathtt{ebeam}}{10 \ m_{\text{u,ion}} \ T_e}
\mathtt{xj} = \sqrt{\mathtt{xjs}}
\mathtt{yj} = 0.8 \frac{Z_{\text{eff}}}{m_{\text{u,ion}}}
\mathtt{rjfunc} = \frac{\mathtt{xjs}}{((4.0 + 3.0\mathtt{yj} + \mathtt{xjs}(\mathtt{xj} + 1.39 + 0.61\mathtt{yj}^{0.7})))}
\mathtt{epseff} = \frac{0.5}{A}
\mathtt{gfac} = \left(1.55 + \frac{0.85}{Z_{\text{eff}}}\right)\left(\sqrt{\mathtt{epseff}}-\left(0.2+\frac{1.55}{Z_{\text{eff}}}\right)\mathtt{epseff}\right)
\mathtt{ffac} = \frac{1}{\mathtt{zbeam}} - \frac{(1-\mathtt{gfac})}{Z_{\text{eff}}}
\mathtt{abd} = 0.107 (1-0.35 \ \mathtt{alphan}+0.14 \ \mathtt{alphan}^2)(1-0.21 \ \mathtt{alphat})(1-0.2\times 10^{-3}\mathtt{ebeam}+0.09\times 10^{-6} \ \mathtt{ebeam}^2)
\text{Current drive efficiency [A/W]} = \mathtt{abd} \times\frac{5}{R_0} \times0.1\frac{\mathtt{ten}}{n_{\text{e},20}} \times \frac{\mathtt{rjfunc}}{0.2}\mathtt{ffac}

  1. N. A. Uckan and ITER Physics Group, "ITER Physics Design Guidelines: 1989", ITER Documentation Series, No. 10, IAEA/ITER/DS/10 (1990) ↩