Specificity of Boundary Conditions for Laser-Stimulated …
291
P c V
(c)
= ν R T c in place of V
(c)
we will get an estimation: P c = ρ 0 R Γ T c /μ, and a
sufficient condition for a flow q s will look in this case like
q s >
ρ 0 R Γ T c c
μ
·
1
1 + R
.
In practice, such estimation is interesting for an initial flow q, which is related to
the flow q s which passed in a solid by correlation q s = (1 − R)q. Then for the initial
value of flow, we get
q >
ρ 0 R Γ T c c
μ
·
1
1 − R 2 .
After this equation, estimations were made for concrete materials. They show
that, for example, for aluminum the superficial value of stream must meet condition q ≥
6×10
13
1−R 2 W/cm
2 , for copper and chrome q ≥
9×10
13
1−R 2 W/cm
2 for tungsten q ≥
1.5×10
14
1−R 2 W/cm
2 , for titan q ≥
7.6×10
13
1−R 2 W/cm
2 , and for potassium q ≥
4×10
12
1−R 2 W/cm
2 .
As evidently, such estimations do not contradict experimental information [11].
Consequently, here we will name flows intensive, if they meet condition got before.
3 Dynamics of Formation of Processes Caused by Intense
Laser Irradiation on the Surface of the Substance
Traditionally, the problems of the destructive and non-destructive interaction of a
powerful impulse in the flow of energy from the surface are regarded as different.
However, assuming that each of the coexisting phases is already a continuous
medium, the system of equations, describing them, will be common to both, namely
[12]
∂ρ
∂t
+ div(ρv) = R m ,
(1)
dv
i
dt
+ (v · ∇)v
i
−
1
ρ
∂ P i j
∂ x j
= f
i
,
(2)
ρ
dU
dt
+ ρ(v · ∇)U + divQ = P i j v i j .
(3)
In this system, U, ρ, v are, respectively, intrinsic energy of the continuous medium
mass unit, density of this medium, and a convection velocity vector, Q is general
energy flow in the medium, P i j is a stress mechanical tensor pressure, v i j =
∂v i
∂ x j
is
strain velocity tensor, {i, j} = {1, 2, 3}.
291
P c V
(c)
= ν R T c in place of V
(c)
we will get an estimation: P c = ρ 0 R Γ T c /μ, and a
sufficient condition for a flow q s will look in this case like
q s >
ρ 0 R Γ T c c
μ
·
1
1 + R
.
In practice, such estimation is interesting for an initial flow q, which is related to
the flow q s which passed in a solid by correlation q s = (1 − R)q. Then for the initial
value of flow, we get
q >
ρ 0 R Γ T c c
μ
·
1
1 − R 2 .
After this equation, estimations were made for concrete materials. They show
that, for example, for aluminum the superficial value of stream must meet condition q ≥
6×10
13
1−R 2 W/cm
2 , for copper and chrome q ≥
9×10
13
1−R 2 W/cm
2 for tungsten q ≥
1.5×10
14
1−R 2 W/cm
2 , for titan q ≥
7.6×10
13
1−R 2 W/cm
2 , and for potassium q ≥
4×10
12
1−R 2 W/cm
2 .
As evidently, such estimations do not contradict experimental information [11].
Consequently, here we will name flows intensive, if they meet condition got before.
3 Dynamics of Formation of Processes Caused by Intense
Laser Irradiation on the Surface of the Substance
Traditionally, the problems of the destructive and non-destructive interaction of a
powerful impulse in the flow of energy from the surface are regarded as different.
However, assuming that each of the coexisting phases is already a continuous
medium, the system of equations, describing them, will be common to both, namely
[12]
∂ρ
∂t
+ div(ρv) = R m ,
(1)
dv
i
dt
+ (v · ∇)v
i
−
1
ρ
∂ P i j
∂ x j
= f
i
,
(2)
ρ
dU
dt
+ ρ(v · ∇)U + divQ = P i j v i j .
(3)
In this system, U, ρ, v are, respectively, intrinsic energy of the continuous medium
mass unit, density of this medium, and a convection velocity vector, Q is general
energy flow in the medium, P i j is a stress mechanical tensor pressure, v i j =
∂v i
∂ x j
is
strain velocity tensor, {i, j} = {1, 2, 3}.