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1, 120103 (2012)

. , , . , 600000, , . . 87. ( 9.05.2012; 10.09.2012) - . . , . , . , . . - .
PACS: 82.20.Wt. : 539.216.1; 517.958:531.12. : , , .

. . , . . , . . , . . , . . , . .

-- . . [1, 2] , . . . , . - .
1.

. 1.

E-mail: kucherik@vlsu.ru

YAG:Nd3+ 1.06 . 5 50 , ( , h 25µm, d 400 , H = 500 ) 100 , , , 0.1 1 , 20 . - . , , , . 50 200 , . , (200500 ) , . . , , 150 . , 1-2 30 . 2, 3 , .

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. ( ) 1 2 2 - = + y x x y Re x2 y 2 2 2 + = - y 2 x2 = x , - = y , y x -- , -- ,x , y -- . , : vx (x ,y ) = 6y (1 - y ), vy (x ,y ) = 0 (1)

. 1: : 1 -- ; 2 -- , , ; 3 -- , ; 4 -- ( -- d), (5); 6 -- ; H -- ; h -- ; 7 -- ( hc dc )

(x ,y ) = 6(2y - 1),

(x ,y ) = y 2 (3 - 2y ),

- , .
2.

, . [3, 4]. . , . [5]. [6]. , . 4. -

x -- , y -- . -- = 0 = 1 , . , . , , : (q1 ,q2 ) (q ): q = q1 + q2 . [7] . , (xi ,yk ) : i,k = - 3 ( hx2
i+1,k

-

i,k

1 )- 2

i+1,k

.

(xi ,yk )
i,k

=-

3 ( hx2

i-1,k

-

i,k

1 )- 2

i-1,k

.

(xi ,yk ) :
i,k

=-

3 ( hy 2

i,k-1

-

i,k

1 )- 2

i,k-1

.

. .

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. 2: : ) ; )

. 3: (); dc = 5 , hc = 3 ()

: ( + B 1 i ) 1 + Reu+ 1/2 hx , i- hx2 |hx ) 1 + + Revk-1/2 hy , hy 2 |hy
i,k i-1,k

= A1

+1,k

A1 = A2 =

(

1 1 1+ 2 Re|u 1 1+ 1 Re|v 2

i-1/2

+ A2 i,k ( B1 = B2 = (

-1

+ B2

i,k+1

, |hx |hy - Re u- /2 i+1 hx

1 1 1+ 2 Re|u

i+1/2

)

k-1/2

1 1+ 1 Re|v 2

k+1/2

- Rev

- k+1/2

hy

)

1 , hx2 1 , hy 2

C = A1 + B1 + A2 + B2 , u v
i+1/2

k+1/2

- i+1,k-1 - 4hy i-1,k+1 +i-1,k - i+1,k+1 - = 4hx { 1 u , + u = (u + |u|) = 0 , 2 =
i+1,k+1

+

i,k+1

i,k-1 +1,k

, ,

ui v

-1/2

= =

i-1,k+1 i-1,k-1

+

i,k+1

i

+ {

k-1/2

i-1

u0 u<0

u- =

1 (u -|u|) = 2

0, u,

- i-1,k-1 - i,k-1 , 4hy ,k - i+1,k-1 - i+1,k , 4hx u 0 , u < 0

hx, hy -- , ui+1/2 , ui-1/2 , vk+1/2 ,vk-1/2 -- (xi , yi ), A1 , B1 , A2 , B2 -- .

: ( ) 2 2 + 2 i,k = hx2 hy i-1,k +i+1 = hx2

,k

+

i,k-1

+ hy 2

i,k+1

+

i,k

.

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. , . + - (. . u+ ,v 0, u- ,v 0, -- , -

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, . . ), . . :

s+1 i,k

= (1 - q )

s i,k

+ q

(

1 hx

2

(

s+1 i-1,k

+

s i+1,k

)

(

+
2 hx

1 hy
2

2

+

(

2

s+1 i,k-1

2 hy

)

+

s i,k+1

)

s+1 + i,k

)

,

s+1 i,k = (1 - q )

s i,k

+q

(

A1

s+1 i-1,k

+ B1

s i+1,k

+ A2 C

s+1 i,k-1

+ B2

s i,k+

)

,

s -- , q , q -- . , q = q = 1 , , s+1 (xi ,yk ) s+1 i,k i,k s s i,k , i,k . , i, k . , . , « » . , . , . , :
s+1 i,k s = (1 - q )i,k + ( 3( + q - 2 hy

: max( , ) < = 10
s+1 s s = max | i,k - i,k |/ , i,k

-3

-10

-4

,

= max |
i,k

s+1 i,k

-

s i,k

|/s , |
s i,k

s =

i,k

|

s i,k

|/M ,

s =

i,k

|/M ,

M -- . , [4]: ) ( )7 ( ( )6 du 1 1 (x - xi ) = 2 -1 dt ri ri ri ) ( )7 ( ( )6 dv 1 1 y = 2 -1 dt ri ri ri x(0) = x0 , dx = u, dt y (0) = y0 , dy = v, dt u(0) = u0 , v (0) = v0 .

s+1 i,k-1

-

s+1 i,k

)

1 - 2

s+1 i,k-1

)

,

. , : . , (s+1) --

x, y -- , u, v -- 0 0 ,
2

r = (x - xi ) + y 2 -- i- . ,

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[5]. , .

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max 2, max -- ; -- .

u

k+1/2

- uk

-1/2

=

i

fix (ri );

k

f

ix

=

(

1 ri k (

)( ) )7 ( ( )6 xk - xi 1 2 -1 ; ri k ri k 1 ri k ) )7 ( ( )6 1 yk 2 -1 ; ri k ri k
k+1/2

v

k+1/2

-v

k-1/2

=

i

fiy (ri );
k+1/2

k

f

ix

=

x

k+1

- xk =u

;

y

k+1

- yk =v

,

k = 1, 2, .. -- , -- k- . t = 0.50 u1/2 - u0 = fix ; 0.50 i v
1/2

- v0 = fiy . 0.50 i

, , k- , , . 3 (k ), . , (x) 2 . e = |x( ) - x(2 ) |/3.
3.

. 4:

, 2 . . 4 , . : d1 = 1, d2 = 0.1. r1 = 0.1 r2 = 0.5. , -, . , -

. (Re). , , -- (. 5). , , . , , . . 4 AB. , 5 . , , . -

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. 5: ) Re=10: d1 = 1, d2 = 1; ) Re=10: d1 = 1, d2 = 1.4 ) Re=50: d1 = 1, d2 = 0.1

, . . 4 FH. (Re) 1.
1: (. . 4) Re 10 50 100 500 1000 AO 0.08 0.07 0.06 0.05 0.05 OB 0.21 0.15 0.12 0.07 0.06 OF 0.40 0.37 0.36 0.27 0.25 BF 0.19 0.22 0.23 0.20 0.19

, -

-- . , , . . , . . 4 C. , , 2 50 . . . ,

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, . . . , , , , , . , , . -- (t) -- , [5, 8]. ( ) : l = 3 · 10-10 , t = 10-12 , v = 500 /. . 2.
2: y 2 3 4 5 10 20 30 40 50 u0 = 0, v0 = 0 t0 9.1 3.91·101 1.08·102 2.36·102 2.70·103 3.32·104 1.53·105 4.56·105 1.11·106 u0 = 1 , v 0 = 0 x 9.1 3.91·101 1.08·102 2.36·102 2.70·103 3.33·104 1.51·105 4.56·105 1.09·106

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. y 1.5 4 vmax = 0.28 vmax = 0.35. y 4 50 vmax 0.35 1 %. , « » , , . (ymax ) . , , . , . , x = u · t0 . ymax 30 40, u = 1 -- 40 110 , . Re=50 ymax = 30 : r1 = 150 - 40 = 110 , r2 = 370 + 40 = 410 . ymax = 40 : r1 = 10 , r2 = 510 . , r1 100 , r2 500 . , (. . 1). (. 6) , , . , . , . , -- . . , , , .

t1 9.1 3.92·10 1.08·10 2.36·10 2.70·10 3.33·10 1.51·10 4.56·10 1.09·10

1 2 2 3 4 5 5 6

. 2 (y ), -- (t0 ) , -- , -- u0 = 1, v0 = 0. , y > 2 v = 0 x = u · t0 .

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. 6: ) Re=1000 4 ; ) Re=1000 4

, : , . . 23 ; , . , , . , . , , .

. . , . . , .

[1] Arakelian S.M., Kutrovskaya S.V., Kucherik A.O. et al l. Proc. SPIE 6732. 67320A. (2007). [2] .., .., .., .., .. . 38, 1. . 7376. (2008). [3] .., .., ... . . . (.: «», 2008). 320 . [4] .. . . (.: , 2007). 84 .

[5] .. . 2. . (: : , 2006). 156 . [6] .. .(.: , 2003). 840 . [7] . : . . (.: , 1980). 616 . [8] .. . (.: , 2008). 616 .

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Numerical mo delling of propagation pro cess and sedimentation of ablated particles in the scheme of a direct laser dusting
. . Antip ov, S. M. Arakelyan, D. N. Buharov, S. V. Kutrovskaya, A. O. Kucherik, V. G. Prokoshev
Department of Physics and Applied Mathematics, Faculty of Physics and Applied Mathematics, A.G. and N.G. Stoletov Vladimir State University. Vladimir 600000, Russia. E-mail: kucherik@vlsu.ru. In the given work results of experimental and theoretical researches of processes of distribution and sedimentation of the lazer-induced plasma in a problem of a direct laser dusting are considered. Researches were spent at influence of laser radiation on a carbon target in the presence of atmospheric air. The special experimental scheme has been developed for management of process of distribution of plasma, allowing to create gasdynamical channel with changeable geometry. Research of a surface of a cold substrate after laser influence has allowed to define presence of various zones of the sedimentation which formation can be explained by the features of plasmadynamical processes. For modelling of process of distribution of plasma the mathematical model based on the hydrodynamic approach has been offered. The offered model allows to define arising features in distribution of a stream near to a substrate surface. On the basis of modelling potential Lennard-Jhones with use of formed lines of a current calculations of the sizes of possible areas of sedimentation of products laser blation are carried out. PACS: 82.20.Wt. Keywords: mathematical modelling, laser ablation, sedimentation. Received 9 May 2012.

1. -- ; . (492) 247-96-21, e-mail: aantipov@vlsu.ru. 2. -- .-. , ; .: (492) 253-33-58 e-mail: aarak@vlsu.ru. 3. -- ; . (492) 247-96-21, e-mail: buharovdn@gmail.com. 4. -- ; .: (492) 247-96-21, e-mail: sstella@vlsu.ru. 5. -- .-. , , ; (492) 247-96-21, e-mail: kucherik@vlsu.ru. 6. -- .-. , , ; . (492) 233-52-42 e-mail: prokoshev-vg@vlsu.ru.

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