US 12,768,869 B2 · Method for processing anisotropic magnetized plasma medium and system thereof

Abstract

A method for processing anisotropic magnetized plasma medium and a system thereof are provided. The method includes obtaining the Maxwell equation and the polarization current density equation based on the electromagnetic characteristics of anisotropic magnetized plasma; processing the Maxwell equation and the polarization current density equation to obtain the electric field intensity, the magnetic field intensity, and the polarization current density after processed; based on the electric field intensity, the magnetic field intensity, and the polarization current density after processed, numerical iterative equations for electric field intensity, magnetic field intensity, and polarization current density in anisotropic magnetized plasma medium are obtained; a numerical modeling simulation electromagnetic model is used to determine the electromagnetic characteristics of the electromagnetic model. The use of the present disclosure to simulate the propagation of electromagnetic waves in anisotropic magnetized plasma medium has higher numerical calculation accuracy.

A method for processing anisotropic magnetized plasma medium, comprising:

obtaining a Maxwell equation and a polarization current density equation based on electromagnetic characteristics of anisotropic magnetized plasma;
processing the Maxwell equation and the polarization current density equation to obtain an electric field intensity, a magnetic field intensity, and a polarization current density after processed;
using a matrix exponential time-domain finite difference method to obtain numerical iterative equations for the electric field intensity, the magnetic field intensity, and the polarization current density in anisotropic magnetized plasma medium based on the electric field intensity, the magnetic field intensity, and the polarization current density after processed;
applying a numerical modeling simulation electromagnetic model to determine electromagnetic characteristics of the electromagnetic model according to the numerical iterative equations for the electric field intensity, the magnetic field intensity, and the polarization current density in the anisotropic magnetized plasma medium;
wherein the Maxwell equation is:
∇
×
E
=
-
μ
0
⁢
∂
H
∂
t
;
∇
×
H
=
ε
0
⁢
∂
E
∂
t
+
;
the polarization current density equation is:
dJ
dt
+
v
=
ε
0
⁢
ω
p
2
⁢
E
+
b
×
;
where, E is the electric field intensity, H is the magnetic field intensity, J is the polarization current density, ε0, μ0 are respectively a dielectric constant and a permeability in vacuum, ωp is a plasma frequency, v is a plasma collision frequency, ωb=B0/me is a electron cyclotron frequency, B0 is an external static magnetic field, e is an electron charge, and me is an electron mass;
wherein processing the Maxwell equation and the polarization current density equation to obtain the electric field intensity, the magnetic field intensity, and the polarization current density after processed, specifically comprising:
performing multi-level symplectic discretization on the Maxwell equation and the polarization current density equation to obtain the electric field intensity, the magnetic field intensity, and the polarization current density in a symplectic discretization format:
E
n
+
l
/
m
=
E
n
+
(
l
-
1
)
/
m
+
d
l
⁢
Δ
⁢
t
ε
0
⁢
∇
×
H
n
+
l
/
m
+
-
d
l
⁢
Δ
⁢
t
ε
0
⁢
J
n
+
l
/
m
H
n
+
l
/
m
=
H
n
+
(
l
-
1
)
/
m
+
-
c
l
⁢
Δ
⁢
t
μ
0
⁢
∇
×
E
n
+
(
l
-
1
)
/
m
J
n
+
l
/
m
=
DJ
n
+
(
l
-
1
)
/
m
+
ε
0
⁢
ω
p
2
⁢
FE
n
+
(
l
-
1
)
/
m
,
where, dl and cl are coefficients of symplectic propagator,
Ω
=
[
-
v
-
ω
bz
ω
by
ω
bz
-
v
-
ω
bx
-
ω
by
ω
bx
-
v
]
,
l is a order of a field component Ψ=(H, E, J)T, and m is a number of stages of non-dissipative p-order symplectic integral, D=eCΔt, F=Ω−1(D−I);
wherein using a matrix exponential time-domain finite difference method to obtain numerical iterative equations for the electric field intensity, the magnetic field intensity, and the polarization current density in anisotropic magnetized plasma medium based on the electric field intensity, the magnetic field intensity, and the polarization current density after processed specifically comprises:
assuming that the plasma medium is biased by a static magnetic field in the z-direction, based on the electric field intensity, the magnetic field intensity, and the polarization current density after processed, the matrix exponential time-domain finite difference method is used to obtain numerical iterative equations for the electric field intensity, the magnetic field intensity, and the polarization current density in anisotropic magnetized plasma medium:
E
x
n
+
l
/
m
(
i
+
1
2
,
j
,
k
)
=
E
x
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
,
k
)
+
d
l
⁢
Δ
⁢
t
ε
0
×
{
γ
y
⁢
1
[
H
z
n
+
l
/
m
⁢
(
i
+
1
2
,
j
+
1
2
,
k
)
-
H
z
n
+
l
/
m
⁢
(
i
+
1
2
,
j
-
1
2
,
k
)
]
+
γ
z
⁢
1
[
-
H
y
n
+
l
/
m
⁢
(
i
+
1
2
,
j
,
k
+
1
2
)
+
H
y
n
+
l
/
m
⁢
(
i
+
1
2
,
j
,
k
-
1
2
)
]
+
γ
y
⁢
2
[
H
z
n
+
l
/
m
⁢
(
i
+
1
2
,
j
+
3
2
,
k
)
-
H
z
n
+
l
/
m
⁢
(
i
+
1
2
,
j
-
3
2
,
k
)
]
+
γ
z
⁢
2
[
-
H
y
n
+
l
/
m
⁢
(
i
+
1
2
,
j
,
k
+
3
2
)
+
H
y
n
+
l
/
m
(
i
+
1
2
,
j
,
k
-
3
2
)
]
}
-
d
l
⁢
Δ
⁢
t
ε
0
⁢
J
x
n
+
(
l
-
1
)
/
m
⁢
(
i
+
1
2
,
j
,
k
)
E
x
n
+
l
/
m
(
i
,
j
+
1
2
,
k
)
=
E
x
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
)
+
d
l
⁢
Δ
⁢
t
ε
0
×
{
γ
z
⁢
1
[
H
x
n
+
l
/
m
(
i
,
j
+
1
2
,
k
+
1
2
)
-
H
x
n
-
l
/
m
(
i
,
j
+
1
2
,
k
-
1
2
)
]
+
γ
x
⁢
1
[
-
H
z
n
+
l
/
m
⁢
(
i
+
1
2
,
j
+
1
2
,
k
)
+
H
z
n
+
l
/
m
(
i
-
1
2
,
j
+
1
2
,
k
)
]
+
γ
z
⁢
2
[
H
x
n
+
l
/
m
(
i
,
j
+
1
2
,
k
+
3
2
)
-
H
x
n
+
l
/
m
(
i
,
j
+
1
2
,
k
-
3
2
)
]
+
γ
x
⁢
2
[
-
H
z
n
+
l
/
m
⁢
(
i
+
3
2
,
j
+
1
2
,
k
)
+
H
z
n
+
l
/
m
(
i
-
3
2
,
j
+
1
2
,
k
)
]
}
-
d
l
⁢
Δ
⁢
t
ε
0
⁢
J
x
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
)
E
x
n
+
l
/
m
(
i
,
j
,
k
+
1
2
)
=
E
x
n
+
(
l
-
1
)
/
m
(
i
,
j
,
k
+
1
2
)
+
d
l
⁢
Δ
⁢
t
ε
0
×
{
γ
x
⁢
1
[
H
y
n
+
l
/
m
⁢
(
i
+
1
2
,
j
,
k
+
1
2
)
-
H
y
n
+
l
/
m
(
i
-
1
2
,
j
,
k
+
1
2
)
]
+
γ
y
⁢
1
[
-
H
x
n
+
l
/
m
⁢
(
i
,
j
+
1
2
,
k
+
1
2
)
+
H
x
n
+
l
/
m
(
i
,
j
-
1
2
,
k
+
1
2
)
]
+
γ
x
⁢
2
[
H
y
n
+
l
/
m
⁢
(
i
+
3
2
,
j
,
k
+
1
2
)
-
H
y
n
+
l
/
m
(
i
-
3
2
,
j
,
k
+
1
2
)
]
+
γ
y
⁢
2
[
-
H
x
n
+
l
/
m
⁢
(
i
,
j
+
3
2
,
k
+
1
2
)
+
H
x
n
+
l
/
m
(
i
,
j
-
3
2
,
k
+
1
2
)
]
}
-
d
l
⁢
Δ
⁢
t
ε
0
⁢
J
x
n
+
(
l
-
1
)
/
m
(
i
,
j
,
k
+
1
2
)
H
x
n
+
l
/
m
(
i
,
j
+
1
2
,
k
+
1
2
)
=
H
x
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
+
1
2
)
+
c
l
⁢
Δ
⁢
t
μ
0
×
{
γ
z
⁢
1
[
E
y
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
+
1
)
-
E
y
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
)
]
+
γ
y
⁢
1
[
-
E
z
n
-
(
l
-
1
)
/
m
(
i
,
j
+
1
,
k
+
1
2
)
+
E
z
n
+
(
l
-
1
)
/
m
(
i
,
j
,
k
+
1
2
)
]
+
γ
z
⁢
2
[
E
y
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
+
2
)
-
E
y
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
-
1
)
]
+
γ
y
⁢
2
[
-
E
z
n
-
(
l
-
1
)
/
m
(
i
,
j
+
2
,
k
+
1
2
)
+
E
z
n
+
(
l
-
1
)
/
m
(
i
,
j
-
1
,
k
+
1
2
)
]
}
H
x
n
-
l
/
m
(
i
+
1
2
,
j
,
k
+
1
2
)
=
H
x
n
-
(
l
-
1
)
/
m
(
i
+
1
2
,
j
,
k
+
1
2
)
+
c
l
⁢
Δ
⁢
t
μ
0
×
{
γ
x
⁢
1
[
E
z
n
+
(
l
-
1
)
/
m
(
i
+
1
,
j
+
1
2
,
k
)
-
E
y
n
+
(
l
-
1
)
/
m
(
i
,
j
,
k
+
1
2
)
]
+
γ
z
⁢
1
[
-
E
x
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
,
k
+
1
)
+
E
z
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
,
k
)
]
+
γ
x
⁢
2
[
E
z
n
+
(
l
-
1
)
/
m
(
i
+
2
,
j
,
k
+
1
2
)
-
E
y
n
+
(
l
-
1
)
/
m
(
i
-
1
,
j
,
k
+
1
2
)
]
+
γ
z
⁢
2
[
-
E
x
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
,
k
+
2
)
+
E
z
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
,
k
-
1
)
]
}
H
x
n
-
l
/
m
(
i
+
1
2
,
j
+
1
2
,
k
)
=
H
x
n
-
(
l
-
1
)
/
m
(
i
+
1
2
,
j
+
1
2
,
k
)
+
c
l
⁢
Δ
⁢
t
μ
0
×
{
γ
y
⁢
1
[
E
x
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
+
1
,
k
)
-
E
x
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
,
k
)
]
+
γ
x
⁢
1
[
-
E
y
n
+
(
l
-
1
)
/
m
(
i
+
1
,
j
+
1
2
,
k
)
+
E
y
n
+
(
l
-
1
)
/
m
(
i
,
j
+
1
2
,
k
)
]
+
γ
y
⁢
2
[
E
x
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
+
2
,
k
)
-
E
x
n
+
(
l
-
1
)
/
m
(
i
+
1
2
,
j
-
1
,
k
)
]
+
γ
x
⁢
2
[
-
E
y
n
+
(
l
-
1
)
/
m
(
i
+
2
,
j
+
1
2
,
k
)
+
E
y
n
+
(
l
-
1
)
/
m
(
i
-
1
,
j
+
1
2
,
k
)
]
}
J
x
n
+
l
m
⁢
(
i
+
1
2
,
j
,
k
)
=
[
cos
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
⁢
J
x
n
+
l
-
1
m
(
i
+
1
2
,
j
,
k
)
+
[
sin
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
⁢
J
y
n
+
l
-
1
m
(
i
+
1
2
,
j
,
k
)
+
ε
0
⁢
ω
p
2
⁢
{
v
[
1
-
cos
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
v
2
+
ω
b
2
+
ω
b
⁢
sin
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
v
2
+
ω
b
2
}
⁢
E
x
n
+
l
-
1
m
(
i
+
1
2
,
j
,
k
)
+
ε
0
⁢
ω
p
2
⁢
{
v
⁢
sin
⁢
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
v
2
+
ω
b
2
+
ω
b
[
cos
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
-
1
]
v
2
+
ω
b
2
}
⁢
E
y
n
+
l
-
1
m
(
i
+
1
2
,
j
,
k
)
because a current density position is the same as an electric field position, therefore, when calculating
J
x
n
+
l
/
m
(
i
+
1
2
,
j
,
k
)
,
it is necessary to perform interpolation on
J
y
n
-
l
/
m
(
i
+
1
2
,
j
,
k
)
⁢
and
⁢
E
y
n
-
l
/
m
(
i
+
1
2
,
j
,
k
)
,
because Jy and Ey are no value at a point
(
i
+
1
2
,
j
,
k
)
,
so it needs to be averaged by four adjacent diagonal values to obtain:
J
y
n
-
l
/
m
(
i
+
1
2
,
j
,
k
)
=
1
4
⁢
(
J
y
n
-
l
/
m
(
i
,
j
-
1
2
,
k
)
+
J
y
n
-
l
/
m
(
i
,
j
+
1
2
,
k
)
+
J
y
n
-
l
/
m
(
i
+
1
,
j
+
1
2
,
k
)
+
J
y
n
-
l
/
m
(
i
+
1
,
j
-
1
2
,
k
)
)
E
y
n
-
l
/
m
(
i
+
1
2
,
j
,
k
)
=
1
4
⁢
(
E
y
n
-
l
/
m
(
i
,
j
-
1
2
,
k
)
+
E
y
n
-
l
/
m
(
i
,
j
+
1
2
,
k
)
+
E
y
n
-
l
/
m
(
i
+
1
,
j
+
1
2
,
k
)
+
E
y
n
-
l
/
m
(
i
+
1
,
j
-
1
2
,
k
)
)
J
x
n
+
l
m
(
i
,
j
+
1
2
,
k
)
=
[
cos
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
⁢
J
y
n
+
l
-
1
m
(
i
,
j
+
1
2
,
k
)
+
[
sin
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
⁢
J
x
n
+
l
-
1
m
(
i
+
1
2
,
j
,
k
)
+
ε
0
⁢
ω
p
2
⁢
{
v
[
1
-
cos
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
v
2
+
ω
b
2
+
ω
b
⁢
sin
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
v
2
+
ω
b
2
}
⁢
E
y
n
+
l
-
1
m
(
i
,
j
+
1
2
,
k
)
-
ε
0
⁢
ω
p
2
⁢
{
v
⁢
sin
⁢
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
]
v
2
+
ω
b
2
+
ω
b
[
cos
⁡
(
ω
b
⁢
c
l
⁢
dt
)
⁢
e
-
vc
l
⁢
dt
-
1
]
v
2
+
ω
b
2
}
⁢
E
x
n
+
l
-
1
m
(
i
,
j
+
1
2
,
k
)
because the current density position is the same as the electric field position, therefore, when calculating
J
y
n
+
l
/
m
(
i
,
j
+
1
2
,
k
)
,
it is necessary to perform interpolation on
J
x
n
-
l
/
m
(
i
,
j
+
1
2
,
k
)
⁢
and
⁢
E
x
n
+
l
/
m
(
i
,
j
+
1
2
,
k
)
,
because Jx and Ex are no value at a point
(
i
,
j
+
1
2
,
k
)
,
so it needs to be averaged by four adjacent diagonal values to obtain:
J
x
n
-
l
/
m
(
i
,
j
+
1
2
,
k
)
=
1
4
⁢
(
J
x
n
-
l
/
m
(
i
-
1
2
,
j
,
k
)
+
J
x
n
-
l
/
m
(
i
+
1
2
,
j
,
k
)
+
J
x
n
-
l
/
m
(
i
+
1
2
,
j
+
1
,
k
)
+
J
x
n
-
l
/
m
(
i
-
1
2
,
j
+
1
,
k
)
)
E
x
n
+
l
/
m
(
i
,
j
+
1
2
,
k
)
=
1
4
⁢
(
E
x
n
-
l
/
m
(
i
-
1
2
,
j
,
k
)
+
E
x
n
-
l
/
m
(
i
+
1
2
,
j
,
k
)
+
E
x
n
-
l
/
m
(
i
+
1
2
,
j
+
1
,
k
)
+
E
x
n
-
l
/
m
(
i
-
1
2
,
j
+
1
,
k
)
)
J
z
n
+
l
m
(
i
,
j
,
k
+
1
2
)
=
e
-
vc
l
⁢
dt
⁢
J
z
n
+
l
-
1
m
(
i
,
j
,
k
+
1
2
)
-
e
-
vc
l
⁢
dt
-
1
v
⁢
E
z
n
+
l
-
1
m
(
i
,
j
,
k
+
1
2
)
where, i, j, k represent spatial nodes of electric field, magnetic field, and current density:
γ
x
⁢
1
=
9
8
⁢
1
Δ
⁢
x
,
γ
y
⁢
1
=
9
8
⁢
1
Δ
⁢
y
,
γ
z
⁢
1
=
9
8
⁢
1
Δ
⁢
z
,
γ
x
⁢
2
=
-
1
24
⁢
1
Δ
⁢
x
,
γ
y
⁢
2
=
-
1
24
⁢
1
Δ
⁢
y
,
γ
z
⁢
2
=
-
1
24
⁢
1
Δ
⁢
z
.
wherein the electromagnetic model comprises an anisotropic magnetized plasma slab model, a blunt cone model, and a sphere model.

3,083 more elements

Method for processing anisotropic magnetized plasma medium and system thereof

Life of this patent

Method for processing anisotropic magnetized plasma medium and system thereof

Life of this patent

Abstract

Claims1