Measurement of Screening Enhancement to Nuclear Reaction Rates using a StronglyMagnetized, StronglyC

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Measurement of Screening Enhancement to Nuclear
Reaction Rates using a Strongly-Magnetized,
Strongly-Correlated Nonneutral Plasma

• Dan Dubin, UCSD
• Experimental collaborators
• John Bollinger, Marie Jensen NIST Boulder
• Supported by the NSF/DOE partnership

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How can a nonneutral plasma have anything to do
with nuclear reaction rates??
Nonneutral plasma collection of charges of
like sign eg. pure ion plasma (Be)
pure ion plasmas can be confined for days in the
static electric and magnetic fields of a Penning
trap

• B 4 Tesla
• E 10Volt/cm
• 30 kHz
• n 108 cm-3
• T 0.001K - 104 K

Nuclear reactions are NOT happening.
But something analogous to nuclear reactions IS
happening!
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Nuclear reactions in the sun
Bethe (1939), Gamow and Crutchfield (1949),
Reaction rate n Required distance of closest
approach b a few Fermi, 10-12 cm (nuclei
tunnel the rest of the way through the Coulomb
barrier)
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Ion-Ion Collisions in a strong magnetic field
Low parallel energy (strongly-magnetized
collision)
B
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Higher parallel energy collision
B
Release of cyclotron energy requires close
collisions to break the adiabatic invariant
or
Collision timescale
So K is internal energy, like nuclear energy.
Close collisions release this energy
Gamow peak in equipartition rate will occur if
Eg. B1 Tesla, mmBe , T 6
Equipartition rate n of cyclotron temperature T
and parallel temperature T is analogous to
nuclear reaction rate

ONeil Hjorth 85
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Theory and experiment for equipartition
rate (measured on pure electron plasma)
k-1
Beck, Fajans and Malmberg Phys. Plasmas 96,
Glinsky, ONeil and Rosenbluth Phys. Fluids B 93
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What effect does Debye screening have on the
rate (nuclear or equipartition)?
Debye screening decreases energy required for a
given distance of closest approach b
Salpeter 55
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Screening Enhancement factor f for equipartition
is identical to enhancement factor for nuclear
reactions
Release of cyclotron energy in a close collision
of guiding centers is analogous to release of
nuclear energy in close collision of nuclei
Both nuclear and equipartition rates are enhanced
by screening because close collisions are more
probable when they are screened
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G 1 in a white dwarf, a giant planet interior,
or a nonneutral plasma
f is very large (Salpeter and van Horn, 1969)
and has never been verified experimentally
I. Strong shielding regime close collisions
still dominate
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Rate enhancement due to screening is huge at
large G, Predictions for it differ (dynamical
screening controversy J. Bahcall 2002) f has
never been tested experimentally in the strong
shielding or pycnonuclear regime.
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MD Simulations of equipartition can measure the
rate enhancement factor f(G)
N200 ions, Wc/wp 12.4. Parameters chosen so
that G 1.25/T Start with T T. Increase T
instantaneously, twice.
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Simulation with T As T decreases, n decreases and equilibration is
suppressed
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Measured equipartition rate for several
simulations
no theory for 2-body equipartition rate n
f(G) no
Wc/wp12.4

• 1.25/T,
• k 42.4/T3/2

Dubin, PRL in press
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Experimental evidence of enhanced equipartition
Laser-cooled Be ion cloud, initial T 0.001 K.
At time t0 turn off laser cooling.
Pure Be
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Rapid heating in a dirty cloud
?? 1-10 hertz 1010 ?0
Marie Jensen et al. PRL in press
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Proof that heating step is due to to dark ion
cyclotron motion
Add rf noise to trap electrode at dark ion
cyclotron freq. Parallel energy is heated
resonantly but only when T is sufficiently large
T(t)
T at 1 sec