A.5 Beta limit

Beta limit means there is a limit for the value of beta beyond which the plasma will encounter a serious disruption. Early calculation of the beta limit on JET shows that the maximal β_t obtained is proportional to I_p∕(10⁶aB_t0), where all quantities are in SI units.  This scaling relation β_{t max} = C_TI_p∕(10⁶aB_t0) is often called Troyon scaling, where the coefficient C_T was determined numerically by Troyon to 0.028. Often C_T is expressed in percent, in which case C_T = 2.8. This motivates us to define

(537)

which is called “normalized beta”. The normalized beta β_N is an operational parameter indicating how close the plasma is to reach destabilizing major MHD activities. Its typical value is of order unit.

As mentioned above, β_N calculated by Troyon is 2.8. Empirical evaluation from the data of different tokamaks raises this value slightly to 3.5, although significantly higher values, e.g., β_N = 7.2, have been achieved in the low aspect ratio tokamak NSTX[22].

The value of β_N indicates how close one is to the onset of deleterious instability . The ability to increase the value of β_N can be considered to be the ability of controlling the major MHD instabilities, and thus can be used to characterize how well a tokamak device is operated. One goal of EAST tokamak during 2015-2016 is to sustain a plasma with β_N ≥ 2 for at least 10 seconds.

(check** The tearing mode, specifically the neoclassical tearing mode (NTM) is expected to set the beta limit in a reactor.)

(**check: Tokamak experiments have found that it is easier to achieve high β_N in large I_p plasmas than in small I_p plasmas. However, experiments found it is easier to achieve high β_p in small I_p plasmas than in large I_p plasmas. Examining the expression of β_N and β_p given by Eqs. (536) and Eq. (??), respectively, we recognize that pressure limit should have a scaling of ⟨p⟩∝ I_p^α with 1 < α < 2. )