Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Muon Catalyzed Fusion



On Dec 13, 2007, at 12:42 PM, Faraday321@aol.com wrote:


We are having a discussion on fusion on another list. So I thought this
might be of some "historical interest.


An interesting proposal to greatly improve the reaction rate of
deuterium-tritium fusion is the idea of using heavy electrons ( muons) as Catalysis in
the fusion process. How this works is simple to understand.

Using the simple Bohr model of electron orbits we can see that ( This is
essentially a classical description so it isn't actually correct except as an
illustration.)

F_em= N*hbar*F_cf

Where the N*hbar product is the quantization factor. ( Where N is the
principle Quantum number)

Therefore

Z*e^2/R^2 = N*hbar*( m_e*v^2/R)

Where R is the orbit radius and m_e is the electron mass, Z is the
atomic number and e is the electric charge of the electron.


For hydrogen atoms R is on the order of 1E-10 meters

But by replacing the electron with a muon which is 207 times more massive
than an electron we can see

R=Z*e^2/N*hbar*m_mu*v^2

putting R at the order of 5 E -13 meters.


To generate this process a beam of muons is directed at a frozen mass
of deuterium and tritium. The muon beam is able to displace some of the
electrons making it possible for the deuterium and tritium to get close enough to
significantly increase the probability that the strong nuclear force will
overcome the EM force causing the atoms to fuse. We can write

g_stg*( Q_str_1*Q_stg_2/ R^2) *exp [- m_pion*R*c/h] > g_em*(
Q_em1*Q_em2/R^2)


Though in reality due to tunneling fusion can occur at larger values of R.
After the fusion event the muon is released and can bind with additional
Nucleuses to serve as a catalyst for additional fusion events.

Unfortunately there are practical problems which have prevented the
success of this process. First the muon is not a stable particle and in its own
proper time it has a mean lifetime of only 2.2 E-6 seconds.

Muon= electron + anti- Electron- neutrino + muon-neutrino


So there is a limit as to how many reactions a single muon can mediate. But
an even more serious problem which sabotages this process even if the muon
had a much longer mean decay time is what is called Alpha sticking. Looking
at the fusion reactions we have

1) 1H2+1H2= 1H3+1H1 + 4Mev

2) 1H3+1H1= 2He3 +0n1 +17.6Mev

3) 1H2 +1H2 =2He3 +0n1 + 3.2 Mev

4) 2He3 +1H2 =2He4 +1H1 +18.3Mev


In reactions 2,3,4 we get the creation of helium nucleuses. They are of
course ionized and serve as attractors for the freed muons removing them as a C
atalyst from the reaction chain. The probability of this occurring is about .01
based on measurements made in 1957.( Jackson) So even given a stable muon
each muon can only serve as a Catalyst , on average , for about 100 fusion
events before it is removed from the process by binding to a Helium nucleus.
This is unfortunately only about 1/5 of the number of needed reactions to
break even in terms of input energy , given the most efficient process
currently possible.

However, more recent measurements of the "alpha sticking probability" from
experiments at Los Alamos have put this number as high as 300, unfortunately
still well below the break even value of 500.

Reality of tiny muoninc hydrogen-like atoms was demonstrated by the analysis of their X-ray spactra. The idea of relying on such short-lived atoms, to facilitate spontaneous fusion of hydrogen nuclei (in tiny D2 molecules) was investigated Alvarz. Even without complicating factors (mentioned above) the conclusion was that the half-life of muons is too short for practical applications of the idea. That was about 20 years ago.
_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/