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

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 - 104 K Nuclear reactions are NOT happening. But something analogous to nuclear reactions IS happening!

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:

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

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

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

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

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

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

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

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.

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

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

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

Experimental evidence of enhanced equipartition Laser-cooled Be+ ion cloud, initial T~ 0.001 K. At time t=0 turn off laser cooling. Ion-neutral collisions Causes slow heating Pure Be+ Dirty cloud, dark ions (BeH+ etc)

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

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