Adiabatic cooling of antiprotons.

Abstract

Adiabatic cooling is shown to be a simple and effective method to cool many charged particles in a trap to very low temperatures. Up to 3×10(6) p are cooled to 3.5 K-10(3) times more cold p and a 3 times lower p temperature than previously reported. A second cooling method cools p plasmas via the synchrotron radiation of embedded e(-) (with many fewer e(-) than p in preparation for adiabatic cooling. No p are lost during either process-a significant advantage for rare particles.

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Adiabatic Cooling of Antiprotons
G. Gabrielse,1,*W.S. Kolthammer,1R. McConnell,1P. Richerme,1R. Kalra,1E. Novitski,1D. Grzonka,2
W. Oelert,1T. Sefzick,2M. Zielinski,2D. Fitzakerley,3M.C. George,3E.A. Hessels,3C.H. Storry,3M. Weel,3
A. Mu ¨llers,4and J. Walz4
(ATRAP Collaboration)
1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
2IKP, Forschungszentrum Ju ¨lich GmbH, 52425 Ju ¨lich, Germany
3Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
4Institut fu ¨r Physik, Johannes Gutenberg Universita ¨t and Helmholtz Institut Mainz, D-55099 Mainz, Germany
(Received 1 December 2010; published 15 February 2011)
Adiabatic cooling is shown to be a simple and effective method to cool many charged particles in a trap
to very low temperatures. Up to 3 ? 106? p are cooled to 3.5 K—103times more cold ? p and a 3 times lower
? p temperature than previously reported. A second cooling method cools ? p plasmas via the synchrotron
radiation of embedded e?(with many fewer e?than ? p) in preparation for adiabatic cooling. No ? p are lost
during either process—a significant advantage for rare particles.
DOI: 10.1103/PhysRevLett.106.073002 PACS numbers: 37.10.Mn, 52.25.Xz
Much energy and effort is required to produce modest
numbers of antiprotons (? p)—the stable antimatter nucleon.
Reducing ? p energy to form cold antihydrogen (?H) atoms is
a big additional challenge. Years of effort have gone to-
wards realizing the original proposal [1] to capture cold?H
atoms in magnetic traps for precise spectroscopy and tests
offundamental symmetries. The latest significant step is an
atom confined for a small fraction of a second in 1 of 9
trials [2]. However, greatly improved ? p cooling methods
are needed to attain usable numbers of trapped?H for useful
times in known excitation states and to increase low energy
? p beam luminosity.
Two new cooling methods reported in this Letter to-
gether produce the largest cold ? p plasmas—3 ? 106? p at
3:5 ? 0:7 K. For comparison, evaporative cooling recently
reported inthis journal [3], yielded103times fewertrapped
? p at nearly 3 times the temperature. The central demon-
stration here is of adiabatic cooling. Also crucial is the
embedded e?cooling that prepares the ? p for adiabatic
cooling. Many fewer e?than ? p are used, just the opposite
of the e?cooling method [4] used to obtain all cold ? p and
?Hatomssofar.Thenumberofe?presentduringbothtypes
of cooling, many fewer than the eþused to form?H, should
be small enough to not inhibit?H production. Even lower
? p temperatures should be possible with embedded e?
cooling, followed by adiabatic cooling, followed by evapo-
rative cooling.
Adiabatic cooling in a harmonic trap potential takes
place when the restoring force F and potential energy
well U are reduced while these confine a plasma initially
at temperature Ti. A measure of F and U is the oscillation
frequency f of the plasma’s center of mass in the
well, since ! ¼ 2?f determines F ¼ ?m!2z and
U ¼ m!2z2=2. Adiabatic cooling takes Tito Tfas fiis
reduced to ff.
For a low particle density, adiabatic cooling of ? p oscil-
lators [5], implications for the energy analysis of the first
trapped [6] and electron-cooled [4] ? p, and cooling of hot
ions [7] have been considered. A particle oscillator’s en-
ergy E decreases as its oscillation frequency f is reduced
adiabatically because E=f is a familiar adiabatic invari-
ant—the invariant quantized in quantum mechanics. The
prediction is thus Tf¼ ðff=fiÞTi. If a coupled oscillatory
motion contributes heat capacity but no additional cooling
(e.g., ? p cyclotron motion), then the individual particle
prediction is Tf¼ ðff=fiÞ1=2Ti.
The density of the plasmas for this demonstration is
high enough to make the Debye length smaller than the
plasma size. The plasmas are weakly correlated, with a
kinetic energy larger than the Coulomb repulsion energy
between neighboring ? p, on average. The ? p within the
plasma thus move and collide within the plasma boundary
approximately as an ideal gas (viewed in the appropriate
rotating reference frame [8]). The prediction for an ideal
gas [8,9] is
Tf¼ ðVi=VfÞ2=3Ti:
(1)
Adiabatic cooling takes place when the restoring force
does negative work on the plasma to increase its volume
V and decrease its temperature T, all with no entropy
change.
The adiabatic condition for low ? p density is that f
changes very little during an oscillation period, _f=f ?
f. For a dense ? p plasma, a plasma has been changed
adiabatically and reversibly if its final temperature Tf
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is independent of the rate at which f is changed. For all
densities, the adiabatic cooling and the measurement
of Tfmust take place before any other process changes
the plasma temperature (e.g., embedded e?cooling).
The Np¼ 2 ? 105to 3 ? 106? p used for the trials
reported here are accumulated from1 to21injection pulses
of ? p from CERN’s unique Antiproton Decelerator. The
trapping [6], electron cooling [4], and stacking [10] meth-
ods that have accumulated up to 1:1 ? 107? p at ATRAP are
those employed for all ? H experiments [11]. The ? p slow
within a thin degrader window, are captured in a trap
formed by biasing electrodes that surround the ? p, and
cool via collisions with a large number of surrounding
e?. Typically Ne¼ 108photoelectrons are used after
they are liberated from a metal surface by intense ultra-
violet pulses from an excimer laser [12]. A ‘‘rotating wall’’
drive [13] compresses a spheroidal e?plasma to a 2 mm
radius, and the plasma cools via e?synchrotron radiation.
After ? p are loaded they cool via collisions with the
cold e?. Centrifugal forces on the simultaneously rotating
? p and e?plasmas separate them radially [14] so the ? p are
farther from the trap axis.
Directly manipulating trapped ? p, measuring their tem-
perature, and using them for experiments is difficult if
Ne? Np, as in standard e?cooling.?H production, for
example, would be inhibited if e?substitute for eþin what
would otherwise be the replacement collisions [15] that
form more deeply bound?H atoms. The inverted situation
for embedded e?cooling, with Np? Neand each e?
surrounded by many ? p, cools ? p much more slowly but no
less effectively. To investigate embedded e?cooling, most
of the e?are ejected along the trap’s center axis using a
method introduced along with e?cooling [4]. The depth
of the trap containing the ? p and e?is pulsed to 0 eV.
The pulses are long enough that e?thermal velocities can
take them out of the well before the well is restored, but
short enough that the heavier ? p cannot escape. Three or
four pulses leave all of the ? p in the trap, along with
Ne¼ 6 ? 103or 9 ? 102e?(estimated from observed
heating rates below). After the ejection raises the ? p tem-
perature to typically hundreds of K, embedded e?cooling
cools the ? p by an order of magnitude in temperature.
The ? p and remaining e?are confined in a potential well
made by biasing gold-plated, copper ring electrodes
[Fig. 1(a)] with a B ¼ 3:7 T field along their symmetry
axis. The electrodes shown are part of a stack of 39
electrodes (represented fully in [16]). The potential applied
to electrode LTE2 in Fig. 1(a) determines the empty-trap
well depth W0[e.g., Figs. 1(b) and 1(c)] and also the small-
amplitude oscillation frequency f for a single ? p in the
otherwise empty well. (Thus f characterizes an empty
well rather than being defined as an oscillation frequency
of a trapped plasma.) Plasma space charge reduces the
energy required for a ? p to escape the plasma and trap
(along the z axis) to W ? W0[Fig. 1(c)]. The dependence
of W on W0and f, along with Npand plasma geometry, is
calculated with finite difference methods [17].
The small number of e?embedded within the ? p cool or
heat the plasma to a temperature Ti. This steady state Tiis
determinedbyblackbodyradiationfromthetrapelectrodes
and by electrical noise that drives the particles directly.
The time scale for embedded e?cooling is that required to
cool Npantiprotons via the synchrotron radiation of Ne
electrons, each at a rate ?c¼ 4r0!2
(Here r0is the classical electron radius, !cis the e?
cyclotron frequency, and c is the speed of light.) On
average, a ? p in the plasma thus cools at the rate ?p¼
?cNe=Np. The assumption that the energy of the ? p is
transferred to the e?via collisions at a rate ?ep? ?p,
justified below, is possible since ð?pÞ?1? 17 s for our
trials. The coupled rate equations that describe the ? p and
e?temperatures [5] simplify to equal ? p and e?tempera-
tures T, with dT=dt ¼ ??pðT ? TiÞ. For times t ?
ð?pÞ?1, the ? p and e?share the steady-state temperature
Ti. Adiabatic cooling to T < Tiis observed if cooling is
complete and T measured in time t ? ð?pÞ?1.
Collision rates within the plasma are fast compared to
?p. For B ¼ 0, a classic treatment [18] gives a ? p ? e?
collision rate 106times larger than ?pfor our plasmas. The
rate for collisions that couple radial and axial energy is
suppressed when a strong B is added along the trap axis
[19]. Even with the predicted suppression by a factor of
103, the axial-radial collision rate is much faster than ?p,
with a time constant shorter than 0.01 s for even our lowest
temperatures. Since the biggest effect of B is to inhibit the
axial-radial coupling, we assume that the ? p ? e?collision
rate ?epis also larger than ?pby at least 3 orders of
magnitude.
Adiabatic cooling starts with an initial fichosen to be
between 3 MHz and 90 kHz, corresponding to W0between
800 and 0.4 eVon axis. The initial fiis lowered to ff, the
latter corresponding to a well depth W just big enough to
keep ? p from escaping. The adiabatic cooling is completed
c=3c ¼ ð0:2 sÞ?1.
440 420 400 380 360 340 320
b
20
10
10
0
10
20
label
y axis label
z^
B
404
10
0
z cm
eV
2
z cm
0
0
0.2
0.4
eV
W0
W
LTE3
LTE2
LTRW LTCE
ac
FIG. 1.
location of the ? p plasma. (b) On-axis potential energies for ? p on
the trap axis for W0of 0.2, 9, and 77 eV. (c) Expanded view
without (solid curve) and with (dashed curve) the space charge
potential energy for Np¼ 5 ? 105.
(a) Cross section of labeled trap electrodes with the
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in hundreds of ms, with the cooling result the same when
this time is varied by a factor of 5. The cooling time is
short compared to ð?pÞ?1, so that embedded e?cooling
has negligible effect during adiabatic cooling.
The ? p plasma temperature after adiabatic cooling is
revealed [20] by the first few thousand ? p that escape (too
few to modify T) as W0is reduced linearly at 2:2 eV=s to
thevalue at which ? p escape, at a W0that corresponds to ff.
Thermal energy allows the initial ? p to escape over the
potential barrier, along ^ z to the left in Figs. 1(b) and 1(c).
Over the range of the plasma temperatures in this Letter, ff
(determined mostly by space charge) varies by ?2%. The
number escaping, dNp, for a series of small reductions in
the empty-trap well depth, dW0, is counted as a function of
W0. Surrounding scintillators detect ? p annihilations with a
75% efficiency. Each ? p loss spectrum in Fig. 2(a) shows
the first antiprotons escaping as a sharp edge to the right
[expanded examples in Fig. 2(b)]. The edges are at larger
W0for larger Np. Variations of about 10 meV, from varia-
tions in Npand the plasma radius, are small and do not
change the slope of the edges. For a Boltzmann distribu-
tion, lnðdNp=dWÞ / ?W=kT. The conversion between W
and W0used to convert the measured dNp=dW0comes
from the finite difference calculations. If space charge is
neglected (i.e., W ¼ W0assumed), the incorrectly deduced
T for Np¼ 5 ? 105would typically be 1.3–2 times larger,
the latter for the lowest temperatures.
Adiabatic cooling produces the lowest ? p temperatures
directly measured, T ¼ 3:5 ? 0:7 K (the gray band of
Fig. 3 for fi> 400 kHz). Before leveling off at this value,
the measured T fits to a power law in fifor the well within
which embedded e?establish initial equilibrium at Ti¼
31 K. (A noise drive applied to a nearby electrode in-
creases Tito this easily observed value from what other-
wise would be 17 K.) The frequency ffdescribes the well
from which ? p begin to escape. The uncertainties on the
points indicate measurement reproducibility.
What prevents observed temperatures that are even
lower is not yet understood. One possibility is that the
lowest measured T (the same for all Np, Ti, and fi>
400 kHz utilized) is a measurement limit for the apparatus
and method.The actual ? ptemperatures could then be much
lower, as low as 0.4 K if the best-fit power law is extrapo-
lated to the largest fiused. However, no physical cause for
such a limit has yet been identified. A second possibility is
that some technical noise keeps the ? p from reaching a
lower T, but the source of such noise has not yet been
found. A third possibility is that the better theoretical
understanding needed for adiabatic cooling will reveal a
slope change at fi? 400 kHz in Fig. 3.
The cooling in Fig. 3 is more effective than predicted for
small ff=fi. The ideal gas prediction uses Eq. (1) with
plasma volumes from the finite difference calculations for
realistic trap potentials. The prediction does not change
noticeably when the volumes are approximated as sphe-
roids [21] (the required plasma shape within an electro-
static quadrupole potential). Of course, the ? p plasma is not
an ideal gas of constant density within sharply defined
boundaries. The density actually drops off over a
temperature-dependent Debye length that has yet to be
included in the theoretical description. Also compared
in Fig. 3 are predictions T / f?1
familiar adiabatic invariant of an oscillator.
An important feature of adiabatic cooling is that no
particlelossis expected orobserved.Thismakesitpossible
to cool large numbers of ? p. This is important for low
energy ? p experiments given that ? p are not readily avail-
able. For example, the long term goal of trapping?H atoms
for precise laser spectroscopic comparisons to hydrogen
atoms [1] requires as many cold atoms with energies below
0.5 K as possible. This energy is the depth of the deepest
magnetic traps for?H atoms that can be constructed with
state-of-the-art superconducting technology. Larger num-
bers of colder ? p would seem to be a necessary (though
not sufficient) step towards useful numbers of trapped?H
atoms.
Figure 4 illustrates the slow return to equilibrium at
Tiafter adiabatic cooling. The rate ?pis faster with more
i
and T / f?1=2
i
from the
a
2x105
5x1051x106
2x106
3x106
0 100200 300400500 600700
101
102
103
104
well depth W0 meV
well depth W0 meV
dNpdW0 meV
time
b
101
102
103
104
dNpdW0 meV
time
3 K
9 K
21 K
Np
5x105
2 meV
well depth W0 meV
5x1051x106
2x106
3x106
1
1
FIG. 2 (color).
Npas W0is reduced linearly in time (i.e., right to left). (b) T is
determined from the exponential slope of the first thousand ? p to
escape as W0is reduced. The three examples are aligned so the
slopes can be readily compared.
(a) Superposition of ? p loss spectra for indicated
1002005001000 2000
2
5
10
20
1251020
fi kHz
temperature T
K
fiff
3.5
0.7 K
fi
1.2
fi
1
ideal gas
fi
1 2
FIG. 3.
after adiabatic cooling. The measured T fits a power law (solid
curve) down to the lowest T measured (gray band).
Measured and predicted temperatures for 5 ? 105? p
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e?(after 3 rather than 4 ejection pulses). An exponential fit
determines Nein terms of the separately measured Np
since ?p¼ ?cNe=Np. Both curves in Fig. 4 rise to the
same Ti, suggesting that e?rather than ? p are being heated
to make Ti> 1:2 K (the electrode temperature [22]). A
consistent ?pcan be similarly and independently deter-
mined from the T measured as ? p cool to Ti.
The embedded e?cooling of
Ti¼ 17 K is also important on its own, e.g., to remove
heat added when particles are moved to new locations.
Reducing noise that heats the e?(perhaps from radio or
TV stations, or from the many electrical signals in the
decelerator hall) should make Tiapproach the 1.2 K elec-
trode temperature, and an even lower T after subsequent
adiabatic cooling.
Finally, adiabatic cooling is naturally compatible with
producing?H that can be trapped insofar as the ? p rotation
velocities are low in the shallow well at the conclusion of
the cooling.?H formed with such velocities could be cap-
tured a magnetic trap.
In conclusion, adiabatic cooling is shown to be an ef-
fective method for cooling far more ? p than have previously
been cooled. The ? p are cooled to T ¼ 3:5 ? 0:7, the lowest
directly measured ? p temperature. Adiabatic cooling thus
promises to be an important method to attain usable num-
bers of?H atoms that are cold enough to be confined in a
magnetic trap. The ? p are prepared for adiabatic cooling
using embedded electron cooling. This cooling method,
shown to cool many ? p with much fewer e?, has some
promise on its own. Orders of magnitude more cold ? p are
produced by embedded electron cooling followed by adia-
batic cooling than by evaporative cooling, in part because
the latter requires significant particle loss. Embedded
electron cooling, followed by adiabatic cooling, followed
by evaporative cooling should give much lower
temperatures.
We are grateful to CERN for the 5-MeV ? p from its
Antiproton Decelerator. This work was supported by the
NSF and AFOSR of the U.S., the BMBF, DFG, and DAAD
of Germany, and the NSERC, CRC, CFI, and ERA of
Canada. W.O. is supported in part by CERN.
? p that establishes
? p
*ATRAP Spokesperson.
gabrielse@physics.harvard.edu
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6 x 103electrons
9 x 102electrons
0 20 4060 80 100
0
5
10
15
20
25
30
time s
temperature T K
FIG. 4.
rium at Tiis slowly reestablished at a rate ?pthat increases with
Ne. The T ¼ 2:5 K at the left is consistent with best fit of the
measured T in Fig. 3.
After adiabatic cooling of 5 ? 105? p, thermal equilib-
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