John Walk
I-Mode Energy Confinement Modeling (doctoral thesis)
John Walk
The I-mode is a promising new operating regime for tokamak fusion reactor designs. As a component of my thesis research, I developed the first comprehensive study of the pedestal structure in I-mode, using a series of dedicated experiments on MIT’s Alcator C-Mod tokamak. In conjunction with this, my thesis work included an examination of the impact of the pedestal on global energy confinement in I-mode - the understanding of which is essential for extrapolating the regime to reactor-scale tokamaks.
The I-mode’ strong temperature pedestal supports very high core temperatures relative to comparable H-modes, such that at moderate densities the I-mode can attain competitive core pressure (thus fusion power density) despite the relaxed, naturally-stable pedestal.
However, due to the markedly different physics governing the temperature pedestal and energy confinement in I-mode, previously-established empirical trends for energy confinement time in L-mode and H-mode (termed the ITER89 and ITER98 scalings, respectively) must be supplemented with a new scaling for I-mode confinement. These empirical scalings take the form of a power law based on a number of engineering parameters, in the form
for plasma current Ip, applied magnetic field BT, average density ¯ne, machine major radius and aspect ratio R and ε, plasma elongation κ, and heating power Ploss (which also accounts for changes in the thermal stored energy in the plasma).
To conduct this analysis of I-mode data, I used a straightforward linear regression analysis of the logarithm of the power law (allowing for a wide range in the fitting parameters to be included), built on a flexible script producing a power-law model for an arbitrary set of input parameters. For a first pass, I began with the included parameters from the ITER98 H-mode scaling. However, the machine size and plasma shaping parameters must immediately be discarded, as the input parameters from a single tokamak experiment vary far too little to produce a meaningful result (the ITER89 and ITER98 scalings were conducted on an extensive multi-machine database - I am currently assembling I-mode data from other devices to extend my own confinement database). Dropping these parameters results in an “irreducible-complexity” power-law fit suitable for single-machine use on C-Mod data, shown below as (b):
The results from this fit are shown below, for the merged databases including older data from both magnetic-geometry configurations(“rev-B” and “for-B”).
These parameter exponents are shown compared to the results from the ITER89 and ITER98 scalings below. The I-mode scaling is notable for its substantially stronger magnetic-field dependence, and much weaker degradation of energy confinement with increased heating power.
This is consistent with observed physics properties in I-mode - the weak degradation of τE with heating power is indicated by the strong response of the temperature pedestal (which is, fundamentally, representative of a barrier to energy loss). The strong dependence on magnetic field may be tied to the effect of increased field on transition thresholds between L-, I-, and H-mode - increased magnetic field tends to suppress the transition to conventional H-mode (which is ordinarily the upper bound of the operating range in I-mode), thus allowing the operator to push the plasma more aggressively without triggering the H-mode.
The implications of this new scaling for larger tokamaks may be examined by making an estimate of the machine-size dependence in the scaling (which we omitted due to the negligible variation in input parameter values). Initial indications using I-mode data from the ASDEX Upgrade (AUG) tokamak in Germany suggests a size dependence similar to that in the H-mode (ITER98) scaling. Using this estimate, I-mode confinement levels may be extrapolated to other major tokamaks:
The scaling reasonably captures the range of I-mode confinement data from ASDEX Upgrade, while also capturing the comparatively poor confinement initially observed in I-mode experiments on the DIII-D tokamak in San Diego (the H98=1 line indicates the H-mode confinement prediction for identical input parameters). However, when extended to large, high-power, higher-field devices (JET in the UK, and the ITER tokamak currently under construction in France), the strong field dependence and weak degradation of τE with heating power dominates the scaling, resulting in predicted energy confinement well in excess of H-mode levels - an exciting result suggesting that I-mode operation could lead to more compact, economical, high-field/high-power tokamak fusion power plants.