M. Asif / Natural Science 2 (2010) 95-97

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97

The Assumption 16 that the product of the square of

the major radius and the internal energy is a constant, is

quite stringent as taking this to be a constant, the ﬁrst

driving term in the Grad-Shafranov equation becomes

just proportional to the ﬂux derivative of the logarithm

of the major radius, which shows a rather weak depend-

ence. Therefore, this assumption seems to drastically

narrow down the range of equilibrium conﬁgurations to

which it is applicable. On the other hand, it has been

observed [6] that a high density region appears near the

inside limiter, which means that the density proﬁle at the

inside and outside of plasma along a ﬂux surface is

asymmetric. The pressure is calculated as the product of

experimental temperature and density. Since the internal

energy is related to the pressure as 1

P

u

, we can say

that the pressure distribution is nonuniform poloidally

and the pressure is higher at the inside of plasma than at

the outside. The result is, however, consistent with our

expectation. On the other hand, density and pressure

proﬁle widths are clearly correlated [7].

3. CONCLUSIONS

In summary, we derived the reduced MHD Equations

(18-22) by using the Assumption 16 about the internal

energy in a large aspect ratio limit. These equations in

clude all terms of the same order as the toroidal effect

and only involve three variables, namely the ﬂux, stream

function and internal energy. These equations can be

used to investigate the time evolution of tearing mode

for the high

, large aspect ratio limit for tokamak

Plasmas.

REFERENCES

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[3] Strauss, H.R. (1983) Finite-aspect-ratio MHD equations

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Physics Fluids, 20(8), 1354-1360.

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