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Culham Lower Hybrid | cullhy()

  • iefrf/iefrffix = 6

This routine calculates the current drive parameters for a lower hybrid system, based on the AEA FUS 172 model. AEA FUS 251: A User's Guide to the PROCESS Systems Code AEA FUS 172: Physics Assessment for the European Reactor Study1

  1. Call the lhrad() method to calculate the lower hybrid wave absorption radius, rratio.
  2. Calculate the penetration radius, rpenet, by multiplying rratio with the minor radius of the plasma.
  3. Calculate the local density, dlocal, using the nprofile() function from the profiles_module module. This function takes into account various plasma parameters such as the density profile, electron density at the edge, pedestal density, separatrix density, and the value of the parameter alphan.
  4. Similarly, calculate the local temperature, tlocal, using the tprofile() function from the profiles_module module. This function considers parameters such as the temperature profile, electron temperature at the edge, pedestal temperature, separatrix temperature, alphat, and tbeta.
  5. Calculate the local toroidal magnetic field, blocal, using the formula bt * rmajor / (rmajor - rpenet). Here, bt is the toroidal magnetic field at the magnetic axis, and rmajor is the major radius of the plasma.
  6. Calculate the parallel refractive index, nplacc, which is needed for plasma access. It uses the local density dlocal and the local magnetic field blocal to calculate a fraction frac. nplacc is then obtained by adding frac to the square root of 1.0 + frac * frac.
  7. Calculate the local inverse aspect ratio, epslh, by dividing rpenet by rmajor.
  8. Calculate the LH normalized efficiency, x, using the formula 24.0 / (nplacc * sqrt(tlocal)).
  9. Calculate several intermediate terms, term01, term02, term03, and term04, using different formulas involving nplacc, physics_variables.zeff, tlocal, epslh, and x.
  10. Calculate the current drive efficiency, gamlh, using the formula term01 * term02 * (1.0e0 - term03 / term04).
  11. Return the current drive efficiency normalized by the product of 0.1e0 * dlocal and physics_variables.rmajor.

Lower Hybrid wave absorption radius | lhrad()

This routine determines numerically the minor radius at which the damping of Lower Hybrid waves occurs, using a Newton-Raphson method to establish the correct minor radius ratio. The required minor radius ratio has been found when the difference between the results of the two formulae for the energy E given in AEA FUS 172, p.58 is sufficiently close to zero.

Correction to refractive index (kept within valid bounds) \mathtt{drfind} = \min\left(0.7, \max\left(0.1, \frac{12.5}{\text{te0}}\right)\right)

Use Newton-Raphson method to establish the correct minor radius ratio. The required minor radius ratio has been found when the difference between the results of the two formulae for the energy E given in AEA FUS 172, p.58 is sufficiently close to zero.

Iterate over the following steps to find the minor radius ratio:

  1. Set an initial guess for the minor radius ratio, \mathtt{rat0}, to 0.8.
  2. Repeat the following steps for a maximum of 100 iterations:
    • Calculate the minor radius ratios, r1 and r2, by subtracting and adding 0.1% of \mathtt{rat0}, respectively.
    • Evaluate the function g at \mathtt{rat0}, r1, and r2 using the method lheval(drfind, rat).
    • Calculate the gradient of g with respect to the minor radius ratio, \frac{{dg}}{{dr}}, using the formula \frac{{g2 - g1}}{{r2 - r1}}.
    • Calculate a new approximation for the minor radius ratio, \mathtt{rat1}, using the formula \mathtt{rat0} - \frac{{g0}}{{\frac{{dg}}{{dr}}}}.
    • Ensure that \mathtt{rat1} is within the bounds of 0.0001 and 0.9999.
    • If the absolute value of g0 is less than or equal to 0.01, exit the loop.
    • Update \mathtt{rat0} with the new approximation, \mathtt{rat1}.
  3. If the loop completes all 100 iterations without finding a satisfactory solution, report an error and set \mathtt{rat0} to 0.8.
  4. Return the final value of \mathtt{rat0}.

  1. T. C. Hender, M. K. Bevir, M. Cox, R. J. Hastie, P. J. Knight, C. N. Lashmore-Davies, B. Lloyd, G. P. Maddison, A. W. Morris, M. R. O'Brien, M.F. Turner abd H. R. Wilson, "Physics Assessment for the European Reactor Study", AEA Fusion Report AEA FUS 172 (1992) ↩