The acoustic detection of high-energy particles in water

Volume 70A, number 5,6

PHYSICS LETTERS

2 April 1979

THE ACOUSTIC DETECTION OF HIGH-ENERGY PARTICLES IN WATER V.D. VOLOVIK, A.I. KALINICHENKO, V.T. LAZURIK and G.F. POPOV Received 3 July 1978

The acoustic pulse from an electromagnetic cascade produced by a high-energy particle in water is investigated. An expression which demonstrates the possibilities for acoustic detection ofhigh-energy particles is presented. (The acoustic variant of the DUMAND project.)

It is well known [1] that beams of fast charged particles generate acoustic vibrations in water, In the present paper we investigate the possibilities of acoustic detection of the cascading particle, The following expression for the amplitude of the acoustic pulse was obtained within the thermo-elastic theory [2]:

R

X

f

St

G

U(r0, t) =

2

1/2

2irpS (2r0)

fo (St d~~)

+

4.4~~)~ E \ 2, (2) Pmax(ro, ‘~= r 1/2 (—ii-) dyne/cm 0 10 where.p(r 0)=1;0.95;0.7;0.28;0.12,forr0=50, 100; 250;from 500;the 1000 m, respectively. Thewmaximum distance cascade axis, rm~(E), here de-

1/2

—

112 r’dr’[~(r’,A+(2r0(St—~))

IR —

f..(r’, A

2 (R

—

(2r0(St

—

~))1/2]

/ [(r’)

—

—

and for distances from the cascade axis of 100, 500 and 1000 m (in fig. 1 curves 1,2, 3, respectively); it was calculated using expression (1) and taking into consideration the real acoustic pulse attenuation in ocean water. The maximum values of the acoustic stress for the primary particle energy E = 1016 _.l021 eV can be accurately approximated by the following function:

~)2I 1/2 ~‘

where R is the radius of the heated region and t is the time counted after the pulse has arrived at the point of observation. To carry out the numerical cornputation the expression for the absorbed energy C(r, z) according to the electromagnetic cascade model of Nishimura—Kamata—Greizen and other parameters regarding the ocean conditions at a depth of 5 km were used. The used parameter values were a Grüneisen parameter G = 0,12; sound velocity S = 1.54 krn/s; density p 1 g/cm3. The axial z-coordinate of the point of observation A corresponded to the maximum cascade development (the cascade axis being directed along the z-axis, and the initial point of the cascade being z 0). Fig. 1 illustrates the acoustic pressure P(r 0, t) for an energy of the primary particle of E = 1018 eV

tection offrom the acoustic pulsePis =Pmax(rm~,E), still possible, canwbe obtained the equation here

40

-

30 1 -~

p

20

i_p

10 ~, ~

~

—20

—10

0

~ ___________

—10 Fig. 1.

495

Volume 70A, number 5,6

PHYSICS LETTERS

2 April 1979

P is a noise value. Assuniing, that P is

10001_

determined by

quencies of the pulse under detection to the essential ones by the inequalityf~100 kHz, we obtain P = 9 X l0~ dyne/cm2. The dependence rmax(E) which is shown in fig. 2 makes it possible to estimate the relative the thermo-noise aperture of the of an ocean installation and restricting designedtheforfreacoustic detection of high-energy particles at very

~iooL3

E

1016

1017

high depths of the ocean. References 1018 E 0, eV

Fig. 2.

[1] V.D. Volovik and Gl. Popov, Zh. Eksp. Teor. liz. Pis’ma 1(1975) 601.

[2] A.J. Kalinichenko 65 (1973) 2364.

496

and V.T. Lazurik, Zh. Eksp. Teor. Hz.