INSIGHTS | PERSPECTIVES
sciencemag.org SCIENCEGRAPHIC: C.BICKEL/SCIENCEThe foundation of this treatment rests
on a hierarchy of length scales. The Debye
length lD is the distance over which elec-
trons rearrange their positions so that there
is zero electric field inside the plasma. This
length must be shorter than the extent of the
plasma but longer than the average distance
between ions in the plasma, the so-called
Wigner-Seitz radius aWS. These constraints
ensure that there are many particles in a lD-
sized sphere so that Boltzmann’s statistical
assumptions about collisions will hold. The
Debye length must also be orders of magni-
tude longer than the classic distance of clos-
est approach r 0 , which can be thought of as
the minimum distance between two ions in
a head-on collision.
Treatments like the Boltzmann equa-
tion are valid when lD >> aWS >> r 0. This
regime is that of “ideal” plasmas, and all
plasmas that obey these conditions are
similar. An equivalent way to express these
foundational assumptions in plasma sci-
ence uses characteristic energies instead
of lengths. The average kinetic energy per
particle is approximately KE ≈ kBT, where
kB is Boltzmann’s constant and T is the
plasma temperature. For singly charged
ions, the average nearest-neighbor electri-
cal potential energy per particle is U = e^2 /
(4p « 0 aWS), where e is the electron charge
and « 0 is the permittivity of free space. The
ratio of these two energy scales is called
the strong-coupling parameter G ; U/KE
= r 0 /aWS, basically the cube root of density
divided by temperature. The basic assump-
tion of kinetic plasma theories is that G <<
1, that is, conditions of low density and high
temperature.
When the foregoing hierarchy of length
or energy scales is not met, the plasma is
said to be “non-ideal” or “strongly coupled”
( 5 ). In fusion-class plasmas, for example,
the non-ideal limit is approached in the
early stages of the plasma evolution dur-
ing compression and early heating of the
system, and G ~ 1. The traditional concept
of a collision becomes problematic because
lD ≈ aWS ≈ r 0.
The plasmas created by Langin et al. are
similar to high–energy-density plasmas be-
cause they have comparable values of G ( 6 ).
Thermodynamic properties of plasmas can
be expressed in terms of G, so all plasmas
with a given value of G are thermodynami-
cally similar. Thus, these ultracold neutral
plasmas can help probe the frontier of fu-
sion science (see the figure). Measurements
of collision properties (momentum trans-
fer, thermal relaxation, diffusion, collision
cross sections, Coulomb logarithms, andrelated quantities) can be made in these
low-temperature, low-density plasmas and
then directly applied to computer models of
plasmas with similar values of G.
These plasmas do not constitute the first
laser-cooled ions, which were reported by
the groups of Dehmelt ( 7 ), Wineland ( 8 ),
and others in the 1970s. Nor are these the
coldest ions reported; the ion trapping and
quantum information community achieve
mean temperatures approaching the zero-
point energy of the trap ( 9 ). Ultracold neu-
tral plasmas have also been reported, and
Killian and co-workers have contributed
to the development of this field ( 10 ). These
are, however, the coldest neutral plasmas
yet reported, and neutrality means that the
strong laboratory fields associated with ion
trapping are absent.
The presence of those fields typically
dominates the ion motion for trapped
ions and obscures the underlying inter-
esting plasma physics. Langin et al. haveshown how to laser-cool ions in a neu-
tral plasma, which overcomes a critical
roadblock in the field of strongly coupled
plasma physics. Although photoionized
laser-cooled gases are initiated with essen-
tially zero kinetic energy, the ions instantly
experience strong accelerating forces
from neighboring ions and heat up. This
“disorder-induced heating” limits G to val-
ues near 2 ( 11 ), but laser-cooling the plasma
ions makes it possible to manipulate the
value of G. Thus, collision physics in this
system can serve as a check on benchmark
calculations. It also means these low-
temperature plasmas can be used as simu-
lators for high–energy-density plasmas.
In what seems like a paradox, the ultra-
cold neutral plasmas of Langin et al. can
help us understand collision parameters in
high–energy-density plasma science. Un-
der dense fusion plasma conditions, these
parameters are nearly impossible to mea-
sure directly. Even with the best computer
simulations, it is challenging to compute
the values of these parameters with confi-
dence. Extensions of kinetic theories into
the strongly coupled regime, which are vali-
dated through modeling of plasmas, will fa-
cilitate computer modeling of more complex
and technologically interesting plasmas.
As laser-cooled plasmas become physically
larger or reach longer confinement times, it
may be possible to initiate and study clas-
sic plasma instabilities ( 12 ) or to initiate
and characterize bump-on-tail distribution
relaxations ( 13 ). These systems could also
lead to higher-brightness focused-ion beam
sources ( 14 ), which perhaps could be use-
ful in ion implantation or x-ray source de-
sign. For very large values of G = 172, the
ions will form a Coulomb crystal. Perhaps
in that configuration, it will be possible to
engineer massively entangled states useful
for quantum computation or for high-preci-
sion metrology. jREFERENCES
1. T. K. Langin, G. M. Gorman, T. C. Killian, Science 363 , 61
( 2019 ).
2. P. L. Bhatnagar, E. P. G r o s s, M. Krook, Phys. Rev. 94 , 511
( 1954 ).
3. S. D. Baalrud, J. Daligault, Phys. Rev. Lett. 110 , 235001
( 2013 ).
4. L. G. Stanton, M. S. Murillo, Phys. Rev. E 93 , 043203 ( 2016 ).
5. R. P. D r a k e, High-Energy-Density Physics (Springer, ed. 2,
Heidelberg, 2018 ).
6. T. K. Langinet al., Phys. Rev. E 93 , 023201 ( 2016 ).
7. W. Neuhauser, M. Hohenstatt, P. To s c h e k, H. Dehmelt,
Phys. Rev. Lett. 41 , 233 ( 1978 ).
8. D. J. Wineland, R. E. Drullinger, F. L. Wa l l s, Phys. Rev. Lett.
40 , 1639 ( 1978 ).
9. T. Rosenbandet al., Science 319 , 1808 ( 2008 ).
10. T. C. Killianet al., Phys. Rev. Lett. 83 , 4776 ( 1999 ).
11. Y. C. Chenet al., Phys. Rev. Lett. 93 , 265003 ( 2004 ).
12. P. W. Terry, Rev. Mod. Phys. 72 , 109 ( 2000 ).
13. D. V. D y l o v, J. W. Fleischer, Phys. Rev. Lett. 100 , 103903
( 2008 ).
14. D. Murphyet al., Nat. Commun. 5 , 4489 ( 2014 ).
10.1126/science.aau7988Computational
modelingLaser cooling and
interrogationHigh temperature
and pressureFusionLaser-driven
ignitionLaserHydrogen
iceCold-atom plasmaMaking cold measurements
Spectroscopic studies of cold neutral plasmas allow
measurement of many parameters that are difcult
to obtain from high–energy-density plasmas.
Modeling hot problems
These parameters improve models of laser-driven
nuclear fusion because the two plasmas have
similar parameterized collision rates.What cold plasmas can say about hot ones
The properties of neutral plasmas created by Langin et al. inform models of plasmas at higher temperature and
pressure when they have similar values of the strong-coupling parameter G.
34 4 JANUARY 2019 • VOL 363 ISSUE 6422
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