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In this work capacity of tokamak plasma is calculated using modeling of tokamak configuration as toroidal and coaxial capacitor. This value is very important and plays an important role in time- varying regimes in tokamak. For exact simulation of plasma behavior, this amount will be added to circuit equations and transport codes. Since capacitive properties of tokamak cause production of a radial electric field, it deserves our special attention.

Tokamak is a torodial shape magnetic confinement fusion device that is the best candidate for nuclear fusion reactors [_{θ} which increases the quality of the confinement of tokamak plasmas. The resistive and inductive properties of the plasma in tokamak have been widely studied. Though the plasma has capacitance property in all area between its centre and the chamber wall, its capacitive performance was not widely studied before 1990’s [

Estimation the value of capacitance of the equal circuit of tokamak can be done by a torodial coaxial capacitor (

The Laplace equation [

With substituting the above values in Equation (1) and with respect to that in this system

tion (1) becomes as follows.

Because of the uniqueness of the solutions of Laplace equation, there will be only one answer that will satisfy the above conditions.

It is obvious that in a constant

period is

scribed as a cosine Fourier series of

Now, it is necessary to obtain expressions for

the simplest solution, we first put the

the coefficients of

On the other hand, the solution to Laplace equation for such coordinate system would be in the form of

This solution provides the boundary conditions

With respect to that the boundaries are considered as co-potential surface, on them

electrical charge on each surface of torus is equal to

In this relation

By putting the calculated values for

Since

In limit of

the same formula for capacitance in concentric cylinders. It should be noted that

as

magnetic field, mass density and velocity of light, respectively. Because the values of

The electrical equivalent circuit for tokamak after taking into account the capacitor property is shown in

calculated by

equations,

In Equation (8),

The general solution of Equation (9) for the plasma current can be written as:

In Equation (10)

damping constant, respectively.

rent, respectively.

important factor that can play an important role in various regimes of the tokamak plasma. The values of natural frequencies for different tokamaks are in order of

In fact, according to the properties of electrical elements, in dc regimes (following the end of transient regimes),

The first effects of capacitance are weak damping oscillations with natural frequency in plasma current, radial electric fields and so on, detection of them is usually difficult. Its second effects are to cause some types of fluctuations in density and other plasma parameters at the edge of plasma. Such fluctuations have been observed in Damavand tokamak [

The experimental data of the Damavand tokamak are [

On the basis of dimension and condition of Damavand tokamak we would have:

After some calculating it would be:

And, therefore, it would be:

As previously noted, the first effect of the capacitance is weak damping oscillations with the frequency

In the experiments with Damavand tokamak that a sample of their results is demonstrated in

the negative spike of loop voltage is observed, the disruption instability happened and

damping oscillations. From the calculations using the presented model, it is seen that the frequency of these oscillations is approximately 100 kHz with damping in form of

them is observed [

When a power source (such as induced current, radio frequency wave, neutral beam) is injected into the plasma, there will be two working regimes:

1) The first one is a transient regime in which L and C along with R play role in equation of circuit and to simulate the behaviour of the plasma, using RLC circuit (

2) In the second regime that is a steady state regime, a simple resistive circuit with circuit equation of

Therefore, the capacitance of the plasma like its inductance, plays important role in some working regimes of tokamak. The importance of capacitance properties is not limited to regimes with time-varying loop voltages. In

each transient regime and regimes with time varying power source (such as radio frequency waves and neutral beam heating) the effect of capacitive property can be seen. In

The radial electric field in study of the H mode of tokamak plasmas is a very important parameter and several models have been proposed to explain the origin of them. In this paper, the effects of capacitive property on radial electric field in tokamak are briefly explained. It is proposed that a radial electric field is produced by a ra-

dial current in the form of

Then, a new model for equivalent circuit of tokamak plasmas on the base of capacitive property is explained. The plasma has the capacitive property of

in the form of

value for capacitance in Equation (8) and

In this article, the analysis on the base of this model is first accomplished for Damavand tokamak and a good agreement between results of this model and the experimental results is observed. This model may be extended in future for analysis of the performance of big tokamaks such as ITER.