Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.issp.ac.ru/kafedra/thesis/2012/bachelor/Aleskerov.pdf Дата изменения: Tue Jul 9 11:08:34 2013 Дата индексирования: Fri Feb 28 05:01:40 2014 Кодировка: Поисковые слова: m 8

- ( )

: «TUNING FORK» ( )

822

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. 2012



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I.



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II.



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, . . (, ) . : , . ,

.

=const, div = 0 . 2 . ,
2


. .

, . . , . . , : , , ­gradp = - p. , . ­ . :

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- . (., ). , . , U, , , l (, ). : U2/l. U/l2. ( )

. , - , . ­ ­ . , , . . .
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, , . ( ). 2) -, . , . , , . , . , (, ) L. , , . L ­ , . , , L. , U L , ­ . , . , d . . , . , , ­ (). , , , . , , . , , . l l. , , , . , , , . , «» , . , . 2/3. , l . , . , :

4


, , - . 3) t = 0, , , l(t), : , D, , d. t = t0, D ( ), , .

,

(, ) E(k)dk, k k + dk

k = 2/l(t) C ­ , ~ 1.5. , , k = kd = 2/d. . 2. () -II -. ­ II. , . « » ("vortex tangle"). 1) . || exp(iS)

5


He-II , , . L1 . , , He-II . , : , . (r) -i, ,

m4 ­ 4He. , :

L1, ,

, . , 2 . , , , , n = 0, 1, 2, ... . h/m4 = 9.9810-8 2/ . , L1, . , , . , , L1. , . He-II ; . . He-II . He-II. He-II , , , : rot s = 0. , , . , , . ,
6


s = 0. , rot s = 0, . , , He-II, , , , . , . , , . , , , ( L ). , rot s 0. 2) > 1 1 -II : . , . , . (counterflow turbulence) (Vinen). , , , . (Oregon group) , -II . L . (=L) . ):

1

(

, . ,

, ~

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, , 2L2 , , , -3/2. . -II, , . , 1/k , , . , , 3. . , . ( ). 50 /, . ( .) , / /. , , . , ( ), - ( -I - II). (Awschalom and Schwarz), , , .

D ­ , , a ­ . , , D , . (G. P. Bewley, D. P. Lathrop, and K. R. Sreenivasanan, 2006), . ( 3D) . , -, -II . .
8


III.

,

, He-II : 1. , . , , . , .

, 1 He-II .

2. U- . 3. (Lancaster ­ Pickett's group, Osaka ­ Yano et al.),

9


4.

5.

P. McClintock's group ­ Lancaster, - ( , ) ­ G. Pickett's group - Lancaster

IV.

tuning fork.

Tuning fork , , . :

L, W . (D ­ 2T) , . ( q = 2659 /3) ­ . . , , . . 215 ( 32768 , 32 ) . 105 . ( ).

, , . . ,
10


. , ( ) . , 32 (. .). 32768 1. ?

1) , , 1 . , . 2 / . ( ). . 2) ( ). 4 . , . 3) 2. , F = F0cos(t) , . , m ­ ( ); ­ ; k ­ ; F0 ­ . , . , xa ­ (absorption); xd ­ (dispersion);

11




0

= , ­ . , L, W .

E ­ , Eq = 7.87 1010 /2, mvac = 0.24267 qLWT, q = 2659 /3 ­ ( K.Karrai: 10. K. Karrai and R. D. Grober, Tip-sample distance control for nearfield scanning optical microscopes, in Near-Field Optics, M. A. Paesler and P.T. Moyer (ed.), Proc. SPIE 2535, 69 (1995). K. Karrai, lecture notes (2000) at http://www.nano.physik.uni-muenchen.de/publikationen/Preprints/p-0003Karrai.pd)

3. . U = U0 cos(t) . , ­ , . , , , : , a ­ . K.Karrai

d11 = 2.3110-12 / ­ . 3 a = 2.4710-5 /. , , a . RLC. :

, , , , , a, ,

, . Uo2/(2R) , 2F02/(2m). , , a:

12


R = 2m / a2, . , = , : , 1/R ­ I0(U0), I0 ­ , ­ . m. , - . , , : Ia Id Unipan. 4. , , ( ); -, () , -, - . , , [1]:

mvac ­ , m ­ , fl ­ , fvac ­ . , . [1]

­ , ­ , S ­ , ­ , ( , )

13


V.



1.

Agilent


PI B



Unipan
1

G

1 . Unipan 232B. Unipan GPIB, Agilent 34411A, GPIB . . Agilent . 40 mv pp Unipan 30 mv Agilent 4,222 v, 1 Agilent 9,47 . Unipan 3.16 ( 10). , 1 , . :

: Agilent 34411A, Stanford Research System DS345 : Unipan lock-in nanovoltmetr type 232B, GPIB Agilent USB

14


2. Lab-View

stanford research system ds345 Agilent 34411. , , , . : , . , , . , , , . :

Function : sine, square, triangle, ramp, noise, arbitrary. Number of aver ( , , ). amplitude file , , . , . (Vpp Vrms). Vpp. concatenated string , , , . . . , , . time delay after changing freq , , . , , , . , . (.[7]) ~ 1/, 0/ = 0/. , ~ Q/0 = Q/(2f0). Q~105, , ~ 1 . ( File of Results). , ,
15


, agilent (). (, Unipan, ) . , . , , : , Agilent, ( ). .

, . , , ­ . 3. , , , Ia Id Unipan Ia Id

16


3,0 2,5 2,0

Resonance frequency 32744 Hz, Q-factor 1,6*10

4

The signal from Unipan, V

1,5 1,0 0,5 0,0 -0,5 -1,0 -1,5 -2,0 -2,5 32738 32740 32742 32744 32746 32748 32750 32752

Ia

I

d

Frequency, Hz

4. . 1) f0 = 32987 2) f0 = 39080 3) f0 = 40585 4) f0 = 34716 5) f0 = 36253 7) f0 = 31532,8 8) f0 = 32744 ) f = f = 18 f = 12 f = 11 f = 5,4 f = 1,5 f = 2,0 . Q = Q = 2,2*103 Q = 3,4*103 Q = 3,2*103 Q = 6,7*103 Q = 2,2*104 Q = 1,6*104 ( ) ( ) 12,8 (Vin = 0,15 ) 12,8 (Vin = 0,08 ) 14,3 (Vin = 0,08 ) 11,4 (Vin = 0,08 ) ( ) 8,31 (Vin = 1v) (

3 . 2 4, , , , , 5. ,

. ( 0.01 1.5 , ). ( ) .

17


0 ,8

Resonance frequence 32765 Hz 5 Q-factor 1,1*10

The signal from Unipan, V

The signal from Unipan, V

0 ,6

Tuning fork in vacuum input signal 0.01v 0.02v 0.04v 0.08v 0.16v

7

1,5

6

5

0 ,4

4

3

0 ,2

2

0 ,0

1

32763,0 32763,5 32764,0 32764,5 32765,0 32765,5 32766,0 32766,5

0 32763,0 32763,5 32764,0 32764,5 32765,0

Frequency, Hz

Frequency, Hz

0.01 0.16 , 1

( 0.01 5.12 )

0,20 0,18 0,16

6

Resonance frequence 32757 Hz 4 Q-factor 2,2*10

The signal from Unipan, V

The signal from Unipan, V

0,14 0,12 0,10 0,08 0,06 0,04 0,02 0,00 -0,02 32752 32754 32756 32758

Tuning fork in air input signal 0.01v 0.02v 0.04v 0.08v 0.16v

5

4

Tuning fork in air input signal 0.32v 0.64v 1.28v 2.56v 5.12v

3

2

1

0 32760 32762 32752 32754 32756 32758 32760 32762

Frequency, Hz

Frequency, Hz

0.01 0.16 , 0.32 5.12

, , . , ­ . , , -
10

the signal from unipan, V

1

0,1

ai r v ac uum

0,01 0,01 0,1 1

input signal, V

18


6. , , , , . 39 1)

0,5

Resonance frequency 39104 Hz 3 Q-factor = 2,8 * 10

4,0

0,4

The signal from Unipan, V

The signal from Unipan, V

0,3

In vacuum input signal 0 .0 1 v 0 .0 2 v 0 .0 4 v

3,5 3,0 2,5 2,0 1,5 1,0 0,5

In vacuum input signal 0.08v 0.16v 0.32v

0,2

0,1

0,0
0,0

39060

39080

39100

39120

39140

39160

39060

39080

39100

39120

39140

39160

Frequency, Hz

Frequency, Hz

0.01 0.04 , 0.08 0.32

, R . , . . , .
35 30 25

R = 9 6 8 0 Oh m

Current, µA

20 15 10 5 0 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

Input signal, V

2)
0, 8

Resonance frequency 39100 Hz 3 Q-factor = 2,6 * 10

6

The signal from Unipan, V

0, 6

The signal from Unipan, V

In air input signal 0.01v 0.02v 0.04v 0.08v

5

4

In air input signal 0.16v 0.32v 0.64v

3

0, 4

2

0, 2

1

0, 0

0 39060 39080 39100 39120 39140 39160 39040 39060 39080 39100 39120 39140 39160

39040

Frequency, Hz

Frequency, Hz

0.01 0.08 , 0.16 0.64

19


3)

0,8

Resonance frequency 39096 Hz 3 Q-factor = 2,6 * 10 In He input signal 0.01v 0.02v 0.04v 0.08v

6

5

The signal from Unipan, V

0,6

The signal from Unipan, V

4

I n He input signal 0.16v 0.32v 0.64v

0,4

3

2

0,2

1

0,0

0

39040

39060

39080

39100

39120

39140

39040

39060

39080

39100

39120

39140

Frequency, Hz

Frequency, Hz

0.01 0.08 , 0.16 0.64

,

vacuum air He

Current, µA

10

1

0,01

0,1

Input signal, V

[1]:

, . , . . .
20


, . , , 7. : . , . , . , . 0.01 10. . , . . . .

-0,018

2nd peak
-0,020

The signal from Unipan, V

-0,022

1st peak
-0,024

-0,026

-0,028

-0,030 36000 37000 38000 39000 40000 41000

Frequence, Hz

:

0,005 0,000

1st peak in He-I input signal 0.01v 0.02v 0.04v The signal from Unipan, V

0,6 0,5 0,4 0,3 0,2 0,1 0,0 -0,1

Resonance Frequency 35903 Hz

The signal from Unipan, V

-0,005 -0,010 -0,015 -0,020 -0,025 -0,030 -0,035 -0,040 35840

1st peak in He-I input signal 0.08v 0.16v 0.32v 0.64v

35860

35880

35900

35920

35940

35960

35840

35860

35880

35900

35920

35940

35960

Frequency, Hz

Frequency, Hz

0.01 0.04 , 0.08 0.64

21


8

The signal from Unipan, V

1st peak in He-I input signal 1.28v 2.56v 5.12v 10.0v

4

0

35850

35900

35950

Frequency, Hz

1.28 10

:
2nd peak in He-I input signal 0.08v 0.16v 0.32v 0.64v
The signal from Unipan, V 2nd peak in He-I input signal 1.28v 2.56v 5.12v 10.0v

1 ,0

Resonance Frequency 40195 Hz
0 ,8

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 40140

The signal from Unipan, V

0 ,6

0 ,4

0 ,2

0 ,0

40140

40160

40180

40200

40220

40240

40260

40160

40180

40200

40220

40240

40260

Frequency, Hz

Frequency, Hz

0.08 0.64 , 1.28 10

He-II. , , , . - 15 . . ( 1.85). :

22


0,06

0,04

The signal from Unipan, V

2nd peak
0,02

1st peak
0,00

-0,02

-0,04

-0,06

-0,08 32000 34000 36000 38000 40000 42000

Frequency, Hz

:

0,05 0,04

The signal from Unipan, V

The signal from Unipan, V

0,03 0,02 0,01 0,00 -0,01 -0,02 -0,03 35420 35440 35460

1st peak in He-II input signal 0.01v 0.02v 0.04v

0 ,6 0 ,5 0 ,4 0 ,3 0 ,2 0 ,1 0 ,0 -0,1

Reconance frequency 35466 Hz

1st peak in He-II input signal 0.08v 0.16v 0.32v

35480

35500

35420

35440

35460

35480

35500

Frequency, Hz

Frequency, Hz

0.01 , 0.02, 0.04 ; 0.08 , 0.16 , 0.32

4 12 3

The signal from Unipan, V

The signal from Unipan, V

2

1st peak in He-II input signal 0.64v 1.28v 2.56v

10 8 6 4 2 0 -2

1st peak in He-II input signal 5.12v 10.0v

1

0

-1

-2 35420 35440 35460 35480 35500 35420 35440 35460 35480 35500

Frequency, Hz

Frequency, Hz

0.64 , 1.28, 2.56 ; 5.12 , 10

:

23


0,050 0,045

0 ,6

Reconance frequency 39806 Hz

The signal from Unipan, V

0,040 0,035 0,030 0,025 0,020 0,015 0,010 39780 39790 39800 39810

The signal from Unipan, V

2nd peak in He-II input signal 0.01v 0.02v 0.04v

0 ,5

1st peak in He-II input signal 0.08v 0.16v 0.32v

0 ,4

0 ,3

0 ,2

0 ,1

0 ,0 39820 39830 39840 39780 39790 39800 39810 39820 39830 39840

Frequency, Hz

Frequency, Hz

0.01 , 0.02, 0.04 ; 0.08 , 0.16 , 0.32

16 2 ,5

The signal from Unipan, V

2 ,0

The signal from Unipan, V

2nd peak in He-II input signal 0.64v 1.28v 2.56v

14

1st peak in He-II input signal 5.12v 10.0v

12

1 ,5

10

1 ,0

8

0 ,5

6

39780

39790

39800

39810

39820

39830

39840

39780

39790

39800

39810

39820

39830

39840

Frequency, Hz

Frequency, Hz

0.64 , 1.28, 2.56 ; 5.12 , 10

,

10

The signal from Unipan, V

1st peak i 2nd peak 1st peak i 2nd peak

n normal He in normal He n superfluid in superfluid Turbulent

1

0,1

0,01 0,01 0,1 1 10

Input signal, V

24


, . , , . Ѕ. , Agilent 5 2 . , , 0,5 , ~0,2 . , , ,

. , , . , . 6.1 R = 9680 , = 2f ~ 90 c-1, mvac = 0.24267 LWT, = 4650 /3 ­ , , L W T . [2] : L = 3.12, W = 0.352, T = 0.402 . L ~ 3, T ~ W ~ 0.4 . 510-4 . , a ~ 10-4 /. 1 [1]. , ( ), , [1]. , , . = I/a ~ 0.5 /


: Lab-View ( Ia Id) , , , , , , He-I HeII , , He-II, , () .

25


1. Deepak. Experimental investigation of quantised vortices using grid and quartz tuning forks in superfluid helium-4 in the zero temperature limit. (2010) 2. R. Blaauwgeers, M. Blazkova, M. Clovecko, V.B. Eltsov, R. de Graaf, J. Hosio, M. Krusius, D. Schmoranzer, W. Schoepe, L. Skrbek, P. Skyba, R.E. Solntsev, and D.E. Zmeev. Quartz Tuning Fork: Thermometer, Pressure- and Viscometer for Helium Liquids (2007) 3. .., .. . 6. . 5- . (2001) 4. .. , . . . (1977) 5. . 6. L. Skrbek. The Use of Vibrating Quartz Forks in Cryogenic Helium Research. (2008) 7. . . . . : . 5 . . III. . -- 4- ., . -- .: ; - , 2004.656 .

26