Корпускулярно-фотонные процессы и технологии. Светцов В.И - 83 стр.

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82
   . 3.2  &$
! # &   ".
*   # & ,   & 
 !, ..   , ! +$
 !
∂
∂ ρ
T
t
a T
Q x y z t
c
V
V
− ∇ =
2
( , , , )
, (3.8)
! a, c
V
-  !$ !$ $
#; Q
V
- 6 $ #  ; ρ -
$ #.
0   &  
!    !:
j r j e
r r
( )
/
= ⋅
−
0
2
0
2
, (3.9)
!
j
0
-
$




; r
0
-
&
!

.


(3.6)
.
!
6

#
!
$
!
Q Q e
x
R
e
V V
r
r
Z x
R
= ⋅ −
⋅ − ⋅
−
−
+
0
5
4
8
4
2
0
2
1 3 2 , (3.10)
!
Q
V0
-
6
$
#






.
7
.
(3.10)
$

1
,




$
&!
δ (

.3.3),

!

T(r, x, t)

!
:
T(r x t
Q e
c
x
a t
V
r r
V
, , ) exp
( )
/
=
⋅
⋅
⋅ −
−
⋅
×
0
2
0
2
0
2
2 4ρ
δ
τ
× − ⋅ ⋅ +
⋅ ⋅ ⋅
erfc x a t
x
a x t
dt
m
m
4 1
4
2
2
δ
δ
∆
∆
, (3.11)
!
∆x
m
-
+


!


;
δ≈(0,2-0,4)R.


&

!
!$
$
!
.


!
#
.!"

.
-
&
E
0



δ∼E
0
2
.


+
!$"
(
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)
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;
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.
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,
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$
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!$"
(
."#
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),
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,
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$
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δ
.
+$
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.
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!$
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

. 
                                                                       . 3.2                                     &                                 $
          !                    #                &                                                    "                   .
          *                                      #                 &                                         ,                            &
                         ! ,      . .                                                                ,                       !                    + $
                                 !
                      ∂T           Q ( x , y , z, t )
                         − a 2 ∇T = V                 ,                                                                                       (3.8)
                      ∂t              ρc V
 ! a, cV -                                                                          !            $       ! $                                       $
  #      ; QV -              6                                     $        #                                                                  ; ρ -
         $ #                 .
0                                                                                   &
      !                                                            !            :
                                         2 2
                      j( r ) = j0 ⋅ e − r / r0 ,                                                                                              (3.9)
    ! j0 -              $                        ; r0 - &                                                !                       .
                                  (3.6)          .        !                             6                                                     #
     !            $   !
                                                r2                  5               Z+8 x
                                            −                                               −
                                                r02               x 4
                      Q V = Q V0 ⋅ e                   1−                  ⋅ 3− 2⋅e 4 R ,                                                     (3.10)
                                                              R
    ! QV0 -       6                     $              #                                                                                                   .
       7                .          (3.10)                                               $                            1               ,
                                                                            $               &                !                        δ(          .3.3),
              !                                       T(r, x, t)                            !:
                                                      2       2
                                     Q V 0 ⋅ e r / r0 τ       ( δ − x) 2
                      T(r , x, t ) =                  ⋅ exp −            ×
                                        2c V ⋅ ρ       0
                                                                 4 a ⋅ t

                                                                                    x
                      × erfc − 4δ ⋅ ∆x 2m a ⋅ t 1 +                                                  dt ,                                     (3.11)
                                                                        4a ⋅ ∆x 2m ⋅ δ ⋅ t
 ! ∆xm-       +                                                                         !                                             ;
δ≈(0,2-0,4)R.
                            &                                      !                         ! $                     $           !            .
                             !          #                         . ! "                       . -                            &                             E0
                                                          2
                                                δ∼E0 .
                                                  +                                     !            $" (                !$)
                                                  &                    &                     ;!
           .                  $",                                               $            !+                                           !            $"
(        . "#               $),                                                                              !           ,
             $                                                              δ           .                        + $
           .   $                                                       $                 $+ "                                        $,        &
                                                                                                                 ,                                     $
                             !          $                                               $                                                          .
                                                                   82

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