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Submitted on 1 Jan 1979
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NONLINEAR SOUND INTERACTION IN SUPERFLUID SOLUTIONS
R. Khokhlov, N. Pushkina
To cite this version:
R. Khokhlov, N. Pushkina. NONLINEAR SOUND INTERACTION IN SUPERFLUID SOLUTIONS.
Journal de Physique Colloques, 1979, 40 (C8), pp.C8-239-C8-240. �10.1051/jphyscol:1979841�. �jpa-
00219546�
N O N L I N E A R SOUND INTERACTION IN S U P E R F L U I D S O L U T I O N S R.V. Khokhlov, N.I. Pushkina
Moscow State University
Abstract - We present a thoretical analysis of nonlinear stimulated Raman-type of first sound by temperature waves in 3He - ''He superflind solutions. We show that the sound attenuation in 3He - "He solutions is lower that in pure ''He. The stimulated scattering of first sound by second sound in
3He - "He solutions could be the subject of investigations in experimental nonlinear acoustics.
In the report we present a theoretical analysis of nonlinar stimulated Raman-Type scattering of first sound by temperature waves in superfluid solutions 3 4 He - He /1,2/. Nonlinear Raman-type interactions of first sound with second sound (temperature waves) in superfluids were considered in Ref /3,4/
(in case of pure He and in Ref /5/ in case of He in anisotropic superfluid A-phase.
In solving the problem we start from the two- fluid-model hydrodynamic equations for superfluid solutions /&/. It is convenient to use normal coor- dinates Q, „, chosen in the form :
where
Here P is the pressure, T is the temperature, C is the concentration of He atoms in superfluid He, p , p are the normal and superfluid densities, p is the density, S is the entropy, IL and U„ are the first - and second- second velocities,
We assume plane-wave solutions of the equations for the incident and the scattered sound fields of
the form :
The amplitudes Q , „ are slowly varying functions
0,1,'-
of distance, Q is the pump first sound, Q. is the scattered first-sound wave and Q„ is the second- second wave.
The conditions oo = to^ + GO2, t = It. + t- are assumed to be fulfilled. We obtain the follo- wing equations for the amplitudes Q, 2 :
Q = const.
otj, a2 are the amplitude damping coefficients, JOURNAL DE PHYSIQUE Colloque C8, supplément au n° 11, tome 40, novembre 1979, page C8-239
Résumé.- Nous présentons une analyse théorique de la diffusion non linéaire de type Raman- stimulé du premier son par les ondes thermiques dans des solutions superfluides 3He - "He. Nous montrons que l'atténuation des ondes sonores dans les solutions 3He - ''He est plus faible que dans He pur. La diffusion stimulée du 1er son par le second son dans les solutions 3He - ""He devrait faire l'objet de développements expérimentaux en acoustique non linéaire.
Article published online by EDP Sciences and available at
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979841
JOURNAL DE PHYSIQUE
I n d e r i v i n g the equations ( 1 ) we used t h e i n e q u a l i - t y
3
<< @ which i s t r u e i f t h e c o n c e n t r a t i o n C i s n o t t o o small. I n t h i s case t h e maxing o f pres- sure and temperature i n a mode i s due mainly t o t h e3 4
presence o f He i n s u p e r f l u i d He and n o t t o tem- p e r a t u r e expansion.
The equation ( 1 ) y i e l d t h e f o l l o w i n g expres- sion f o r t h e t h r e s h o l d i n t e n s i t y o f t h e pump sound a t which t h e s t i m u l a t e d s c a t t e r i n g becomes p o s s i b l e
The t h r e s h o l d i n t e n s i t y ( 2 ) i s s i g n i f i c a n t l y lower than t h a t i n pure 'he f o r t i l e two rezsons ;
i n case o f pure 4 ~ e i n debends on t h e q u a n t i t y
$
/2/ which i s lower than t h e q u a n t i t y @ e n t e r i n g the expression ( 2 ) ; besides, t h e sound a t t e n u a t i o n i n 3 ~ e-
4 He s o l u t i o n s i s lower than t h a t i n pure 4 ~ e . Thus t h e s t i m u l a t e d s c a t t e r i n g o f f i r s t sound by second sound i n 3 ~ e-
4 He s o l u t i o n s c o u l d be t h e s u b j e c t o f i n v e s t i g a t i o n s i n experimental n o n l i n e a r acoustics.References
/1/ N.I. Pushkina, R.V. Khokhlov, Proc. o f t h e I X Symposium on Acoustics, Moscow, June, 1977
/2/ V. Lebedev, JETP
3,
2224, 1977./3/ N . I . Pushkina, R.V. Khokhlov Pisma JETP 19, 672, 1974.
-
/4/ V . I . Pokrovsky, I . M . Khalatnikov, JETP - 71, 1974, 1976.
/5/ N . I . Pushkina, R.V. Khoklov, Pisma JETP
3,
N24, 1977.
/6/ i.M. Khalatnikov, "Theory o f S u p e r f l u i d i t y "
"Nauka", M., 1971.
