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Beta Limit

The plasma beta limit1 is given by

\begin{aligned} \beta < 0.01\, g \, \frac{I(\mbox{MA})}{a(\mbox{m}) \, B_0(\mbox{T})} \end{aligned}

where B_0 is the axial vacuum toroidal field. The beta coefficient g is set using input parameter dnbeta. To apply the beta limit, constraint equation 24 should be turned on with iteration variable 36 (fbetatry).

By default, \beta is defined with respect to the total equilibrium B-field 2.

iculbl Description
0 (default) Apply the \beta limit to the total plasma beta (including the contribution from fast ions)
1 Apply the \beta limit to only the thermal component of beta
2 Apply the \beta limit to only the thermal plus neutral beam contributions to beta
3 Apply the \beta limit to the total beta (including the contribution from fast ions), calculated using only the toroidal field

Setting the Beta g Coefficient

Switch iprofile determines how the beta g coefficient dnbeta should be calculated.

iprofile Description
0 alphaj, rli and dnbeta are inputs.
1 (default) alphaj, rli and dnbeta are calulcated consistently. dnbeta calculated using g=4l_i 3. This is only recommended for high aspect ratio tokamaks.
2 alphaj and rli are inputs. dnbeta calculated using g=2.7(1+5\epsilon^{3.5}) (which gives g = 3.0 for aspect ratio = 3)
3 alphaj and rli are inputs. dnbeta calculated using g=3.12+3.5\epsilon^{1.7} 4
4 alphaj and dnbeta are inputs. rli calculated from elongation 4. This is only recommended for spherical tokamaks.
5 alphaj is an input. rli calculated from elongation and dnbeta calculated using g=3.12+3.5\epsilon^{1.7} 4. This is only recommended for spherical tokamaks.
6 alphaj and c_beta are inputs. rli calculated from elongation and dnbeta calculated using C_{\beta}=(g-3.7)F_p / 12.5-3.5F_p, where F_p is the pressure peaking and C_{\beta} is the destabilisation papermeter (default 0.5)5. See Section 2.4 of Tholerus et al. (2024) for a more detailed description. This is only recommended for spherical tokamaks .

Further details on the calculation of alphaj and rli is given in Plasma Current.

Limiting \epsilon\beta_p

To apply a limit to the value of \epsilon\beta_p, where \epsilon = a/R is the inverse aspect ratio and \beta_p is the poloidal \beta, constraint equation no. 6 should be turned on with iteration variable no. 8 (fbeta). The limiting value of \epsilon\beta_p is be set using input parameter epbetmax.

  1. N.A. Uckan and ITER Physics Group, 'ITER Physics Design Guidelines: 1989', ↩

  2. D.J. Ward, 'PROCESS Fast Alpha Pressure', Work File Note F/PL/PJK/PROCESS/CODE/050 ↩

  3. Tokamaks 4th Edition, Wesson, page 116 ↩

  4. Menard et al. (2016), Nuclear Fusion, 56, 106023 ↩↩↩

  5. Tholerus et al. (2024), arXiv:2403.09460 ↩