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Volume 2 - LENR-CANR

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2 16 2<br />

gc<br />

<br />

27 3<br />

So, a solution for the ideal plasma exists. More in detail, we can define:<br />

k k<br />

a <br />

(11)<br />

1 / 2<br />

2 <br />

g0<br />

<br />

3<br />

In this case the coupling critical constant is:<br />

k g0 Ak<br />

(12)<br />

i<br />

A k A<br />

<br />

k g0<br />

k<br />

2<br />

(13)<br />

so to admit the following holding quantity:<br />

A A A A *<br />

* <br />

i<br />

Q A<br />

k Ak<br />

<br />

<br />

k k k k<br />

<br />

<br />

kk<br />

<br />

<br />

*<br />

*<br />

2<br />

(14)<br />

while for the Hamiltonian’s it is easy to compute:<br />

*<br />

*<br />

A A <br />

E<br />

N<br />

p<br />

1<br />

*<br />

H Q A<br />

k A<br />

k ig<br />

2<br />

k k k<br />

<br />

k <br />

<br />

(15)<br />

With the aim of seeing if there are any externals solutions, we write<br />

<br />

k<br />

i<br />

uke<br />

(16)<br />

i<br />

Ak Auke<br />

(17)<br />

where and A are positive constants and uk is a complex vector.<br />

Changing these ones in (12) and (13) we have:<br />

<br />

<br />

2<br />

(18)<br />

A<br />

g0 <br />

(19)<br />

1 2<br />

3 2<br />

<br />

g0<br />

2<br />

0<br />

(20)<br />

and by the condition Q=0 (we cannot have a net charge flow in a plasma), we have:<br />

2<br />

0 1 2<br />

g<br />

<br />

0<br />

In this case it is easy to observe that for<br />

(18) and (19) are satisfied.<br />

g<br />

0<br />

2 <br />

<br />

3<br />

558<br />

1 / 2<br />

it is unlikely that both the equations<br />

(21)

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