In LHD experiments, the highest performance of the energy confinement and beta value is achieved in the so-called "torus-inwardly shifted configuration"[1], where the property of MHD stability is unfavorable. We are interested in the place of the theoretically predicted stability criteria based on the linear MHD unstable modes in experimentally obtained plasmas. Here we analyze the relationship between the experimentally achieved pressure gradients at resonant rational surfaces and the theoretically predicted unstable region for low-n ideal interchange instabilities. According to the analysis of the low-n stability of high beta discharge in a typical "torus-inwardly shifted configuration (Rax=3.6m)", and which corresponds to the best configuration for the achieved energy confinement performance, we find that the low-n ideal interchange mode gives a constraint on the operational regime of the pressure. By using Mercier parameter, DI, the constraint is corresponding to DI~0.3. At the edge region, we have not obtained clear results because the beta value and/or the pressure gradients achieved experimentally are smaller than the beta value where the low-n ideal mode is predicted unstable. According to the analysis of the configurations with wider magnetic hill region, the pressure gradients corresponding to DI>0.5 are achieved in stationary at the core region, which suggests that the criterion depends on the magnetic configurations, for example, the difference of magnetic shear parameter and so on.

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