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4. Error analysis for neutron rate calculations For neutral-beam-heated plasmas the neutron rate depends in a complicated manner on different plasma parameters such as ion and electron temperatures, densities and neutral-beam power. Furthermore, comparatively small changes in these input data can sometimes lead to rather strong changes in the neutron rates. With numerical schemes for calculating neutron rates in the presence of neutral-beam heating it is possible to carry out a sensitivity analysis.
69) Q jv Q js These factors are again functions of all the other plasma parameters. It should be pointed out that the higher the value of one of these factors, the stronger is the neutron rate dependence on the corresponding plasma parameter. Assuming v "0 for simplicity, all possible physically reason able combinations with a sufficient number of data points (reasonable are 5—10) for each parameter in the five-dimensional parameter space Q (¹ ,¹ , n , n , s ) relevant to the experimental regimes " have to be calculated.
This also fixes the ranges of application for an interpretative plasma parameter determination. , ion and electron temperatures ¹ and ¹ , deuteron and electron densities n and n , injection source rate s and toroidal plasma rotation v can be " calculated. Then the relative change in Q is simply ¹ jQ d¹ ¹ jQ d¹ n jQ dn n jQ dn s jQ ds v jQ dv dQ " # # " "# # # . (68) Q j¹ ¹ Q j¹ ¹ Q jn n Q jn n Q js s Q jv v Q " " The sensitivity factors , , ", , and which describe the influence of ion and electron 2 2 temperature, deuteron and electron density, source rate and plasma rotation are ¹ jQ ¹ jQ n jQ n jQ , , , " " " " , " 2 " Q jn Q j¹ Q j¹ Q jn " s jQ v jQ " , " .