# Presentation: 122341

## 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??

- 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!

## Nuclear reactions in the sun 

- Reaction rate **
- Required distance of closest approach *b* ~ a few Fermi, ~10-12 cm
- (nuclei tunnel the rest of the way through the Coulomb barrier)

**Bethe (1939), Gamow and Crutchfield (1949), ...**

## Ion-Ion Collisions in a strong magnetic field

- _Ion-Ion Collisions in a strong magnetic field_

- _Low  parallel energy (strongly-magnetized collision):_

- B

## Release of cyclotron energy requires close collisions

- to break the adiabatic invariant :

- Gamow peak in equipartition rate will occur if

- Eg. *B*=1 Tesla, *m*=*m*Be  ,   *T*<< 3 K

- Collision timescale

- B

- Higher parallel energy collision:

- So K  is internal energy, like nuclear energy.

- or

- Close collisions release this energy

## Equipartition rate  of cyclotron temperature T and parallel temperature T is analogous to nuclear reaction rate:

- 

- O’Neil + Hjorth ‘85

## 

****

- Theory and experiment for equipartition rate
- (measured on pure electron plasma)

- 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*

- 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

## >>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:

## Rate enhancement due to screening is huge at large ,

- Rate enhancement due to screening is *huge* at large ,
- 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*()

- N=200 ions,  c/**p = 12.4.
- Parameters chosen so that  =1.25/*T*
- Start with *T*  >> *T*. Increase *T* instantaneously, twice.

## Simulation with T < T

- As *T* decreases,  decreases and equilibration is suppressed

## o : theory for 2-body equipartition rate

- for several simulations:

- o : theory for 2-body equipartition rate
- *f*o

- c/p=12.4

- = 1.25/T,
-  = 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.

- Pure Be+

## Rapid heating in a dirty cloud

- ~ 1-10 hertz ~ 1010 0

- Marie Jensen et al. PRL in press

## Proof  that heating step is due to to dark ion cyclotron motion  

- _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 *at 1 sec

*T*(*t*)