PLUTO Test Problems
4.4-patch2
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Whistler Waves. More...
Functions | |
void | VectorRotate (double *v, int s) |
The dispersion relation for whistler waves is given by (Huba, 2003):
where is the wave number along the
x
direction, is the domain lenght in the horizontal direction,
and
are the electron charge and number density
B
is the magnetic field strength.
Whistler waves 1 and 2D (SETUP
==
1
)
In configurations #01 and #02 we test the propagation of whistler waves in 1D and 2D, respectively, and the results can be compared with the analytical dispersion relation, in a manner similar to Huba 2003. In 2D, the setup is rotated by an amount proportional to the ratio between the vertical and horizontal axis extents. The magnetic field is in the x-direction, , and the system is perturbed with
and
, where
is the mode number,
G and
G. We also set
.
We show in Fig. 1 the temporal evolution of the perpendicular component of the magnetic field ( ) and the its fourier composition. In Fig. 2 we show the comparison between the analytical and numerical values of the whistler wave frequency as a function of
.
Whistler waves 2D (SETUP
==
2
)
In this section (configuration #02) we test the correct propagation of the whistler waves in 2D, in a manner similar to ViganĂ² et al., 2012. The initial magnetic field is ,
and
, where
and
. Again we set
.
The equations above admit wave solution travelling along with speed
where is the domain length in the vertical direction, and again
is the number of wave modes.
In Fig. 3 we show the result of our simulation ( ) at
. We checked the scaling of the whistler speed with
, shown in Fig. 4.
References:
void VectorRotate | ( | double * | v, |
int | s | ||
) |
Rotate a vector <v[0], v[1], v[2]> based on the domain aspect ratio. s = 1 use normal rotation s = -1 use inverse rotation