Functions
	fclose (file)
	imagesc (kaxis(k_start:k_end) *r_Larmor, waxis(w_start:w_end)/w_ci, log10(abs(Fourier(w_start:w_end, k_start:k_end))))
	colorbar ()
	set (gca, 'YDir', 'normal')
hold on	text ('Interpreter', 'tex')
	xlabel ('{\itk}{\cdot}{\itr}_L')
	ylabel ('\omega/\omega_{ci}')
	plot (kaxis(k_start:k_end) r_Larmor, vA kaxis(k_start:k_end))
	sqrt (1.0+vA vA/(c c))) % Ion-acoustic wave cS
	plot (kaxis(k_start:k_end) r_Larmor, kaxis(k_start:k_end) cS)
	sqrt (1.0+kaxis.kaxis Ldebye2))
	plot (kaxis(k_start:k_end) r_Larmor, kaxis(k_start:k_end) sqrt(kb *Temperature/mp)/w_ci)
Magnetosonic wave	plot (kaxis(k_start:k_end) r_Larmor, kaxis(k_start:k_end) sqrt((cS cS+vA vA)))
	plot (kaxis, kaxis 3 dw sqrt((cS cS+vA *vA)))
	plot (kaxis, kaxis 4 dw sqrt((cS cS+vA *vA)))
	plot (kaxis(k_start:k_end) *r_Larmor, 3)
	plot (kaxis(k_start:k_end) *r_Larmor, 4)
	plot (kaxis(k_start:k_end) *r_Larmor, w_lh/w_ci)
Ion plasma frequency	plot (kaxis(k_start:k_end), w_pi)

Variables
clf ASCII	Vlasiator =load('LDZ2_QPerp_Bxt.dat')
	Real =Vlasiator(:,:)
	Matsize =size(Real)
	lines =Matsize(1)
	cols =Matsize(2)
Binary	file = fopen('Dispersion/LDZ2_QPerp_rhot.bin')
Dropping the last two	numbers
	window = hamming(lines)'
for	i
end Partial plotting	k_start = 2
	k_end = 500
	w_start = 1
	w_end = 500
Parameters	length =2.5e8
	ncells =cols
	dx =length/ncells
	dt =0.04
	Temperature =1.0e5
	B0 = 1.001249e-9
	density = 1.0e3
Constants	c = 299792458.0
	kb = 1.3806505e-23
	mp = 1.67262171e-27
	me = 9.1093826e-31
	q = 1.60217653e-19
	mu0 = 4pi()1.0e-7
	epsilon0 = 8.85418781762e-12
	gamma = 5.0/3.0
	v_th = sqrt(2.0 * kb * Temperature / mp)
	w_ci = q*B0/mp
	r_Larmor = v_th / w_ci
	Fourier =fft2(Real)
	dk =2pi() / (cols dx)
	kaxis =0:dk:cols*dk
	dw =2pi() / (lines dt)
	waxis =0:dw:lines*dw
Alfvén wave	vA = B0 / sqrt(mu0densitymp)
	kaxis2 = kaxis.*kaxis
	kaxis4 = kaxis2.*kaxis2
	de2 = 5314^2
	one = ones(1, cols + 1, 'double')
	omega2Val = 0.5 * (kaxis2 ./ (one + kaxis2 * de2) .* (2.0one + kaxis2 ./ (one + kaxis2 de2)) - sqrt(kaxis4 ./ ((one + kaxis2de2).(one + kaxis2de2).(one + kaxis2de2)) . (4.0kaxis2 + kaxis4 ./ (one + kaxis2 de2))))
	Ldebye2 = epsilon0 * kb * Temperature / (density * q * q)
kaxis, kaxis 2 dw sqrt((cS cS+vA *vA)	plot )()
Numerical propagation	V = dx/dt
Ion lower hybrid frequency	w_ce = q*B0/me
	w_pi = sqrt(density * q^2 / (mp * epsilon0))
	w_pe = sqrt(density * q^2 / (me * epsilon0))
	w_lh = sqrt((w_pi^2 + w_ci^2) / (1 + w_pe^2 / w_ce^2))

Function Documentation

◆ colorbar()

colorbar ( )

◆ fclose()

fclose ( file )

Here is the caller graph for this function:

◆ imagesc()

imagesc	(	kaxis(k_start:k_end) *	r_Larmor,
		waxis(w_start:w_end)/	w_ci,
		log10(abs(Fourier(w_start:w_end, k_start:k_end)))	)

◆ plot() [1/10]

plot	(	kaxis(k_start:k_end) *	r_Larmor,
		3	)

◆ plot() [2/10]

plot	(	kaxis(k_start:k_end) *	r_Larmor,
		4	)

◆ plot() [3/10]

plot	(	kaxis(k_start:k_end) *	r_Larmor,
		kaxis(k_start:k_end) *	cS )

◆ plot() [4/10]

Magnetosonic wave plot	(	kaxis(k_start:k_end) *	r_Larmor,
		kaxis(k_start:k_end) sqrt((cS cS+vA *vA))	)

◆ plot() [5/10]

plot	(	kaxis(k_start:k_end) *	r_Larmor,
		kaxis(k_start:k_end) sqrt(kb Temperature/mp)/	w_ci )

◆ plot() [6/10]

plot	(	kaxis(k_start:k_end) *	r_Larmor,
		vA *	kaxisk_start:k_end )

Here is the call graph for this function:

◆ plot() [7/10]

plot	(	kaxis(k_start:k_end) *	r_Larmor,
		w_lh/	w_ci )

◆ plot() [8/10]

Ion plasma frequency plot	(	kaxis(k_start:k_end)	,
		w_pi	)

◆ plot() [9/10]

plot	(	kaxis	,
		kaxis 3 dw *	sqrt(cS cS+vA vA) )

◆ plot() [10/10]

plot	(	kaxis	,
		kaxis 4 dw *	sqrt(cS cS+vA vA) )

◆ set()

set	(	gca	,
		'YDir'	,
		'normal'	)

Here is the caller graph for this function:

◆ sqrt() [1/2]

sqrt ( 1.0+kaxis.*kaxis * Ldebye2 )

◆ sqrt() [2/2]

sqrt ( 1.0+vA *vA/ c *c )

◆ text()

hold on text	(	'Interpreter'	,
		'tex'	)

Here is the caller graph for this function:

◆ xlabel()

xlabel ( '{\itk}{\cdot}{\itr}_L' )

◆ ylabel()

ylabel ( '\omega/\omega_{ci}' )

Variable Documentation

◆ B0

B0 = 1.001249e-9

Definition at line 41 of file Dispersion.m.

◆ c

Constants c = 299792458.0

Definition at line 45 of file Dispersion.m.

◆ cols

cols =Matsize(2)

Definition at line 8 of file Dispersion.m.

◆ de2

de2 = 5314^2

Definition at line 80 of file Dispersion.m.

◆ density

density = 1.0e3

Definition at line 42 of file Dispersion.m.

◆ dk

dk =2*pi() / (cols * dx)

Definition at line 61 of file Dispersion.m.

◆ dt

dt =0.04

Definition at line 39 of file Dispersion.m.

◆ dw

dw =2*pi() / (lines * dt)

Definition at line 64 of file Dispersion.m.

◆ dx

dx =length/ncells

Definition at line 38 of file Dispersion.m.

◆ epsilon0

epsilon0 = 8.85418781762e-12

Definition at line 51 of file Dispersion.m.

◆ file

Binary file = fopen('Dispersion/LDZ2_QPerp_rhot.bin')

Definition at line 11 of file Dispersion.m.

◆ Fourier

Fourier =fft2(Real)

Definition at line 59 of file Dispersion.m.

◆ gamma

gamma = 5.0/3.0

Definition at line 52 of file Dispersion.m.

◆ i

const int i

Initial value:

=1:cols

Real(:,i) = Real(:, i) .* window

window

Definition Dispersion.m:22

i

for i

Definition Dispersion.m:24

cols

Definition Dispersion.m:8

Real

float Real

Definition definitions.h:41

Definition at line 24 of file Dispersion.m.

◆ k_end

k_end = 500

Definition at line 31 of file Dispersion.m.

◆ k_start

end Partial plotting k_start = 2

Definition at line 30 of file Dispersion.m.

◆ kaxis

kaxis =0:dk:cols*dk

Definition at line 62 of file Dispersion.m.

◆ kaxis2

kaxis2 = kaxis.*kaxis

Definition at line 78 of file Dispersion.m.

◆ kaxis4

kaxis4 = kaxis2.*kaxis2

Definition at line 79 of file Dispersion.m.

◆ kb

kb = 1.3806505e-23

Definition at line 46 of file Dispersion.m.

◆ Ldebye2

Ldebye2 = epsilon0 * kb * Temperature / (density * q * q)

Definition at line 87 of file Dispersion.m.

◆ length

Parameters length =2.5e8

Definition at line 36 of file Dispersion.m.

◆ lines

Using the last two numbers for format lines =Matsize(1)

Definition at line 7 of file Dispersion.m.

◆ Matsize

Matsize =size(Real)

Definition at line 6 of file Dispersion.m.

◆ me

me = 9.1093826e-31

Definition at line 48 of file Dispersion.m.

◆ mp

mp = 1.67262171e-27

Definition at line 47 of file Dispersion.m.

◆ mu0

mu0 = 4*pi()*1.0e-7

Definition at line 50 of file Dispersion.m.

◆ ncells

ncells =cols

Definition at line 37 of file Dispersion.m.

◆ numbers

Dropping the last two numbers

Definition at line 17 of file Dispersion.m.

◆ omega2Val

omega2Val = 0.5 * (kaxis2 ./ (one + kaxis2 * de2) .* (2.0*one + kaxis2 ./ (one + kaxis2 * de2)) - sqrt(kaxis4 ./ ((one + kaxis2*de2).*(one + kaxis2*de2).*(one + kaxis2*de2)) .* (4.0*kaxis2 + kaxis4 ./ (one + kaxis2 * de2))))

Definition at line 82 of file Dispersion.m.

◆ one

one = ones(1, cols + 1, 'double')

Definition at line 81 of file Dispersion.m.

◆ plot

Langmuir wave Light plot(kaxis, kaxis *dw *c) plot % Ion cyclotron frequency plot(kaxis(k_start(kaxis(k_start:k_end) *r_Larmor, 2) ( )

static

Definition at line 92 of file Dispersion.m.

◆ q

q = 1.60217653e-19

Definition at line 49 of file Dispersion.m.

◆ r_Larmor

r_Larmor = v_th / w_ci

Definition at line 56 of file Dispersion.m.

◆ Real

Truncating the first line away Real =Vlasiator(:,:)

Definition at line 5 of file Dispersion.m.

◆ Temperature

Temperature =1.0e5

Definition at line 40 of file Dispersion.m.

◆ V

Numerical propagation V = dx/dt

Definition at line 98 of file Dispersion.m.

◆ v_th

v_th = sqrt(2.0 * kb * Temperature / mp)

Definition at line 54 of file Dispersion.m.

◆ vA

Alfvén wave vA = B0 / sqrt(mu0*density*mp)

Definition at line 77 of file Dispersion.m.

◆ Vlasiator

Vlasiator =load('LDZ2_QPerp_Bxt.dat')

Definition at line 4 of file Dispersion.m.

◆ w_ce

Ion lower hybrid frequency w_ce = q*B0/me

Definition at line 113 of file Dispersion.m.

◆ w_ci

w_ci = q*B0/mp

Definition at line 55 of file Dispersion.m.

◆ w_end

w_end = 500

Definition at line 33 of file Dispersion.m.

◆ w_lh

w_lh = sqrt((w_pi^2 + w_ci^2) / (1 + w_pe^2 / w_ce^2))

Definition at line 116 of file Dispersion.m.

◆ w_pe

w_pe = sqrt(density * q^2 / (me * epsilon0))

Definition at line 115 of file Dispersion.m.

◆ w_pi

w_pi = sqrt(density * q^2 / (mp * epsilon0))

Definition at line 114 of file Dispersion.m.

◆ w_start

w_start = 1

Definition at line 32 of file Dispersion.m.

◆ waxis

waxis =0:dw:lines*dw

Definition at line 65 of file Dispersion.m.

◆ window

window = hamming(lines)'

Definition at line 22 of file Dispersion.m.

Functions

Variables

Function Documentation

◆ colorbar()

◆ fclose()

◆ imagesc()

◆ plot() [1/10]

◆ plot() [2/10]

◆ plot() [3/10]

◆ plot() [4/10]

◆ plot() [5/10]

◆ plot() [6/10]

◆ plot() [7/10]

◆ plot() [8/10]

◆ plot() [9/10]

◆ plot() [10/10]

◆ set()

◆ sqrt() [1/2]

◆ sqrt() [2/2]

◆ text()

◆ xlabel()

◆ ylabel()

Variable Documentation

◆ B0

◆ c

◆ cols

◆ de2

◆ density

◆ dk

◆ dt

◆ dw

◆ dx

◆ epsilon0

◆ file

◆ Fourier

◆ gamma

◆ i

◆ k_end

◆ k_start

◆ kaxis

◆ kaxis2

◆ kaxis4

◆ kb

◆ Ldebye2

◆ length

◆ lines

◆ Matsize

◆ me

◆ mp

◆ mu0

◆ ncells

◆ numbers

◆ omega2Val

◆ one

◆ plot

◆ q

◆ r_Larmor

◆ Real

◆ Temperature

◆ V

◆ v_th

◆ vA

◆ Vlasiator

◆ w_ce

◆ w_ci

◆ w_end

◆ w_lh

◆ w_pe

◆ w_pi

◆ w_start

◆ waxis

◆ window