By Albert R. Baswell
Advances in arithmetic examine offers unique learn effects at the innovative of arithmetic examine. every one article has been rigorously chosen in an try to current gigantic examine effects throughout a vast spectrum.
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Extra info for Advances in Mathematics Research
1ni < v z > ( broken curve), (ni/10 is also plotted for reference). Figure 13. Charge (ni –ne). We plot in Fig. 1 ni < v z > . 1 ni < v z > (here the density ni / 10 is plotted with the dash-three-dots curve to locate the profiles with respect to the gradient). The electric field should interact with the constant magnetic field to give an ExB drift in the poloidal direction ( there is no shear in this drift in the flat part of the electric field, which can explain the absence of turbulence at the plasma edge observed in H-mode tokamaks).
In the present case, we consider a domain with L x = 2π , and L y = 10 . 005 . In as the imaginary part of the domain 0 ≤ x ≤ 2π where the equilibrium flow is defined we have two points of inflexion ω ky located xs = π / 2 at x s = 3π / 2 . and At these points = VD ( x s ) = cos( x s ) = 0 . ; k ys = We perturb the equilibrium ρ 0 as follows: x 2 ρ 0 = sin( x ) + ε sin( ) cos(k y y ) . 015 . Since we are close to a neutrally stable solution, we can use a Taylor expansion to calculate the growth rate of the instability: ω ky = ω ky + (k y − k ys ) ω s , k ys ∂ ∂k y ⎛ω ⎜ ⎜k ⎝ y ⎞ ⎟ .
Hence we have the opportunity to compare two completely different codes, and to evaluate the performance of the cubic spline for the solution of the same problem. In the present cylindrical geometry, the external magnetic field is in the z direction, and ( r , θ ) is the poloidal plane. The plasma is assumed uniform in the z and θ directions. Electrons are magnetized along the magnetic field, and consequently have a constant profile. 20) dv r dvθ We advance Eq. 22) using 1D cubic spline interpolation as discussed * before.