Russian Physics Journal, Vol. 37, No. 6, 1994

P O S S I B L E W A Y S T O A C H I E V E C O L D F U S I O N . I I l

Yu. A. Tisenko UDC 530.4

It is suggested that a deuteron "microaccelerator" be constructed in order to achieve cold fusion. This

accelerator would operate on the basis of a glow discharge near a charged P d - D powder grain in low-density

gaseous D 2. Possible parameters of such an accelerator are calculated. The heat released as a result of fusion

is estimated, as is the intensity of the deuteron flux.

A powder grain of solid palladium (say a small sphere of radius r0) containing dissolved deuterium is charged to a

negative potential [ ~o(ro) [ = 106 V and placed in a chamber with low-density gaseous D 2. A brief glow discharge occurs

near the P d - D grain. If deuterium ions from the gas acquire sufficient velocities over a mean free path, nuclear fusion will

occur when these ions collide with deuterons from the solid palladium.

Let us estimate the minimum radius of the P d - D grains. There are two factors which would limit the number of

electrons on grains of a given radius r o in vacuum. First, there is the increase in electron emission due to tunneling upon an

increase in the absolute value of the potential. The width of the potential barrier at the boundary of the grain decreases as the

result of an increase in the rate of change of the potential at the surface of the grain. The barrier height remains approximately

constant, equal to the work function Awork. The barrier transmission coefficient for electrons is given by

Ktr ~ e x p 3 bee

where E is the field at the surface of the grain, and Awork is the work function. If we set Ktr < 10 -n, then for the selected potential we have

r0~>l.8nlnl0 • 10 -5 m

According to another estimate, the width of the potential barrier is

Ar ~- Awork • r 2 (tceq -- Awork • r0)

where q is the total charge on the grain. Since we have Awork't - h and where v is the electron thermal velocity, the condition for nontransmission through the barrier is

Ar t ~ ~

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or r 0 > > 0.96.10 -5 m. The estimates turn out to be fairly close together. For the calculations below we adopt r = 10 -4 m.

The second factor is the limited number of electron levels in the potential well of radius r o, with a depth on the order

of Awork used to model the palladium grain. The number of levels with a given l is equal to the number of roots of the Bessel

function

ro >> 2hey I ~ (ro) l A = work

J~-~/2 (x) = 0

Dnepropetrovsk Oblast Institute for Continuing Education of Teachers. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 90-93, June, 1994. Original article submitted April 28, 1992.

590 1064-8887/94/3706-0590512.50 ©1994 Plenum Publishing Corporation

r o on the interval 0 < x < x o, where x o = ~ I/" 2m~Awork The number of roots is [11]

Xo 1 2x o in - e; ema x - . .

,~ 2 r:

The maximum possible number of excess electrons in such a well is given by

(x~ . xo'~ 10~2 v:2 .

The number of excess electrons corresponding to the potential [ ~(ro) [ = 106 V is N O = 0.63-1011; this figure is smaller

than N.

Another estimate is based on a statistical formula for the number of electrons:

N - 4p~ r~ hx, P0 = t / ~ e Awork , 3r.h ~

where Ax is the thickness of the electron layer at the boundary of the grain. The number of excess electrons on the grain is

at a maximum when the work performed by the field forces over a distance Ax is equal to the work function:

Ne 2 tc hx ~ Awork r~

From these levels we find

4r~o ( 2m epI2 .AS,2 N2 ~ work, 3=zce'~ h 3

and N = 3.56" 1011. These estimates are very close together.

We now wish to calculate the heat of fusion for one grain, Qf. Deuterons form in gaseous D 2 in the course of the

ionization

D2-~D ° + D + + e-.

We assume that the mean free path in the gaseous D 2 is L > 10r o = 10 -3 m. The potential on the grain is reduced by half upon

the absorption of a number of deuterons K, where

K - 1 rol~(ro) l 0.3 ,1011 2 •e(R + 1) R + I

Here R is the number of electrons which are emitted from the palladium upon the incidence of one deuteron. If the gas pressure

is sufficiently low, the K deuterons will have an average energy E of about 0.75 MeV.

Half the energy of the K deuterons is lost in the Pd over a distance

P. A = ~ 3 . 1 0 -~ m

2pT (3E/4)

where p is the density of the Pd, and T(3E/4) is the stopping power of Pd. Under the assumption that stow deuterons do not

synthesize helium or tritium, we find (% = 3.5 MeV). The energy expended on charging one sphere is

The ratio as a percentage is

Qf ~ ± nD ~o (3E/4) qo •/~ - 2.1

R-¢-1 • 10 r' MeV

We t 1 ro Iv (ro)L 2 - • -- 0.33- 10" MeV 2 rc

Q f . 1 0 0 % = 6.3 i0_~% ~e l R~, I

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This reaction is not a good choice as a heat source, but in a glow discharge the number of neutrons generated over the time

involved in the discharge of one grain in gaseous D 2 is

3 10t N~ ~ and % (3Ei4) K ----- ~ ÷-----~- D

Accordingly, the glow-discharge effect at P d - D powder grains could be utilized to generate a flux of neutrons with

an energy >2.45 Mev.

It would be simpler from the experimental standpoint to arrange a fusion reaction in a "macroscopic" glow discharge

in a discharge tube filled with gaseous D 2 with a palladium cathode, saturated with deuterium. If the length of the discharge

tube were on the order of the deuteron mean free path in gaseous D 2, then at U=0.5 mV the average energy of the deuterons

at the cathode would be E = 0.25 MeV, and the deuterons would loss half their energy in the palladium over a distance A =

0.66.10 -6 m.

The cross section for fusion at an energy 3E/4 is % = 4.8.10-2b. At n D = 7.1028 m-3 the ratio as a percentage is

Qf • 100% - ArtD q0 %. 100% = ~ 1 ' 6 . 10_4oi,, Wet ( R + I ) e U R + 1

and the neutron flux is

N , 1,4 106 j-1 ~"el 14, -b 1

In other words, if R is not too large the discharge tube can serve as a neutron source.

I wish to thank I. M. Ternov, Yu. F. Smirnov, R. N. Faustov, V. Ch. Zhukovskii, D. A. Slavnov, D. D. Ivanenko,

G. A. Sardanashvili, and V. I. Denisov for a discussion of certain aspects of the theory and for support.

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