1. An example of
High Energy Density Physics at
Low Energy Densities
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

2. How can a nonneutral plasma have anything to do with nuclear reaction rates??
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 K
Nuclear reactions are NOT happening.
But something analogous to nuclear reactions IS happening!

3. 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)
Relative Energy E required for close encounter:
n is dominated by superthermal nuclei with E >> T E
e-E/T
s(E) ~ e-c/E
EGamow
1/2
[ c 2 ~ Nuclear Rydberg ~ 105 eV]
Gamow peak:

4. Ion-Ion Collisions in a strong magnetic field
Low parallel energy (strongly-magnetized collision): B E
E||
E +E||
time
No exchange of parallel and
cyclotron energy B E
E||
E +E||
Higher parallel energy:
time
Cyclotron freq. Wc >> all other dynamical frequencies
Energy E of cyclotron motion is an adiabatic invariant
Adiabatic invariant is broken
in close collisions

5. Higher parallel energy collision:B
Release of cyclotron energy requires close collisions
to break the adiabatic invariant : or
Collision timescale
Adiabaticity parameter
So K is internal energy, like nuclear energy.
Close collisions release this energy
In cold, strongly-magnetized plasma, most collisions have
Only superthermal ions release the cyclotron energy
Gamow peak in equipartition rate will occur if
Eg. B=1 Tesla, m=mBe , T<< 3 K

6. Equipartition rate n of cyclotron temperature T and parallel temperature T is analogous to nuclear reaction rate: ^
E||
e-E /T
s(E||) ~ e-c/E
EGamow
3/2 ||
mean adiabaticity parameter
O’Neil + Hjorth ‘85

7. Theory and experiment for equipartition rate
(measured on pure electron plasma)
k-1
Beck, Fajans and Malmberg Phys. Plasmas ‘96,
Glinsky, O’Neil and Rosenbluth Phys. Fluids B ‘93

8. 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
No screening:
Debye screening:
less energy needed to get the same differential rate
enhancement
factor f
rate for no shielding
Salpeter ‘55

9. 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
Eg. in solar interior: n~1023 cm3 T ~106 K G~0.1, f ~1.05

10. f is very large (Salpeter and van Horn, 1969)
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:
interparticle spacing
1<< G << k2/5
Rate is still given by n = f(G) no
(Proof: see
Dubin, PRL in press)
Ichimaru and Iyetomi:
DeWitt and Slattery:
Pycnonuclear regime: G > k2/5 : theory TBD

11. 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.

12. MD Simulations of equipartition
can measure the rate enhancement factor f(G)
N=200 ions, Wc/wp = 12.4.
Parameters chosen so that G =1.25/T
Start with T >> T. Increase T instantaneously, twice. no
n = f(G) no
Rapid equipartition
when T ~ 0.2

13. Simulation with T < T
As T decreases, n decreases and equilibration is suppressed

14. Measured equipartition rate for several simulations:
no : theory for 2-body equipartition rate
n = f(G) no
Wc/wp=12.4
f = n/no
= 1.25/T,
k = 42.4/T3/2
Dubin, PRL in press

15. Experimental evidence of enhanced equipartition
Laser-cooled Be+ ion cloud,
initial T~ K.
At time t=0 turn off laser cooling.
Ion-neutral collisions
Causes slow heating
Pure Be+
Dirty cloud, dark ions
(BeH+ etc)

16. Rapid heating in a dirty cloud
Parallel Temperature jump
due to coupling to hot cyclotron motion
of dark ions
~ 1-10 hertz ~ 1010 0
Marie Jensen et al. PRL in press

17. 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