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Superfluid helium and cryogenic noble gases as stopping media for ion catchers
Purushothaman, Sivaji
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2008
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Purushothaman, S. (2008). Superfluid helium and cryogenic noble gases as stopping media for ion
catchers s.n.
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List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.1
3.2
3.3
3.4
3.5
Density-normalized zero field electron mobilities µ0 N in helium as a
function of temperature [88]. . . . . . . . . . . . . . . . . . . . . . . . .
Density-normalized zero-field mobility of electrons (µ0 N) vs. gas number density (N) of helium for various gas temperature values. . . . . .
Drift velocity vd and density-normalized mobility µN of electrons in
helium as a function of the ratio E/N [28, 82, 88]. . . . . . . . . . . . .
Maximum value of the ratio E/N which can define the value of µ0 in
inert gases as a function of temperature. . . . . . . . . . . . . . . . . .
Electron temperature Te and characteristic energy hei for electrons in
helium as a function of the ratio E/N for gas temperatures Tg = 300 K,
77 K, and 4.2 K as determined from measurements of Dt /µ [8, 36]. . .
Momentum transfer cross section σm of electrons in helium as a function of the electron energy hei [28, 29, 75, 83]. . . . . . . . . . . . . . .
Ion current ratio (iHe2+ )/i(He3+ ) as a function of E/N at 76 K and
1.3 mbar (1.09 × 1017 cm−3 )[54]. . . . . . . . . . . . . . . . . . . . . . . .
The observed reduced mobility µred corresponding to an equilibrium
mixture of He2+ , He3+ and He4+ as a function of E/N at 77 K for four
values of neutral densities [54, 86]. . . . . . . . . . . . . . . . . . . . . .
Collisional radiative recombination rate coefficient α for rare gases
recombining in helium as a function of helium density N [129]. . . . .
Specific heat capacity c p of liquid helium at saturated vapor pressure
as a function of temperature T [14]. . . . . . . . . . . . . . . . . . . .
Relative density of the normal and superfluid components in superfluid helium as a function of temperature T [14]. . . . . . . . . . . . .
Entropy S of superfluid helium as a function of temperature T [14].
Second sound velocity Css as a function of temperature T [14]. . . .
Schematic representation of a snowball. . . . . . . . . . . . . . . . . .
109
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7
8
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10
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15
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25
List of Figures
110
3.6
3.7
Schematic representation of a bubble. . . . . . . . . . . . . . . . . . .
Variation in the density ρ of liquid helium near a localized point
charge [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Zero field mobilities µ0 of positive ions and electrons in liquid helium
as a function of inverse temperature 1/T [89]. . . . . . . . . . . . . .
3.9 Drift velocity vd of positive and negative ions as a function of the
electric field E [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 The critical velocity vr for the production of vortex rings by positive
ions as a fucntion of normal-to-total density ratio ρn /ρ [17]. . . . . .
−1
3.11 Inverse relative mobilities µrel
= µ He+ /µion of positive ions as a
function of temperature T. . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Recombination coefficient of ions in superfluid helium αSF as a function of the inverse temperature 1/T [21]. . . . . . . . . . . . . . . . .
. 25
. 26
. 28
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0
3.13 A point charge Q and the induced image charge Q (at the superfluid
helium-vapor interface). Fim is the image charge force experienced by
the point charge Q. QE is the electric force experienced by the point
charge Q due to the applied electric field E . . . . . . . . . . . . . .
3.14 Electric potential energy φ of a unit point charge Q as a function of
the distance z from an abrupt superfluid-vapor helium interface. . .
3.15 Spatial variation of the dielectric constant e and the density ρ at a
superfluid-vapor helium interface. . . . . . . . . . . . . . . . . . . . .
3.16 Image charge potential energy φim of a unit point charge calculated
for the model interface demonstrated in Figure 3.15 [103]. . . . . . .
4.1
4.2
4.3
4.4
4.5
4.6
Cryostat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Decay chain of 227 Ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic diagram of 223 Rn source preparation setup. . . . . . . . .
A typical energy calibration plot. . . . . . . . . . . . . . . . . . . . . .
A 215 Po α-decay line fitted with a Gaussian line shape and a Gaussian
with low-energy exponential tail (see Equation 4.3). . . . . . . . . . .
4.7 Gaussian with low-energy exponential tail for different distances dx
from its center to the start of its exponential tail. The low-energy tail
arises from the energy loss due to multiple scattering. . . . . . . . .
4.8 A typical α-particle energy spectrum and its analysis. . . . . . . . . .
4.9 Ratio of the warm volume pressure (Pw ) to the cold volume temperature (Tc ) as a function of Tc during cooling down, normalised to the
ratio before cooling down starts (P0 /T0 ). . . . . . . . . . . . . . . . .
4.10 Density relative to the room temperature value in the warm and cold
volumes as a function of the cold volume temperature Tc for different
warm to cold volume ratios Vw /Vc . . . . . . . . . . . . . . . . . . . .
. 33
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45
46
47
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List of Figures
111
4.11 Cold volume density nc /Vc relative to its room temperature value at
a cold volume temperature Tc of 78 K as a function of warm to cold
volume ratio Vw /Vc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
6.1
6.2
6.3
6.4
Photograph of the off-line experimental setup. . . . . . . . . . . . . .
Schematic view of the off-line experimental cell. . . . . . . . . . . . .
Measured efficiency egas as a function of temperature T. . . . . . . .
Efficiency for 219 Rn ion survival and transport in helium gas over a
wide range of density, temperature and electric field in the vicinity
of the 223 Ra source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Photograph of the on-line setup. . . . . . . . . . . . . . . . . . . . . .
Schematic view of the on-line experimental cell. . . . . . . . . . . . .
The combined efficiency of ion survival and transport as a function
of ionization rate density for different electric fields in the ionization region for temperatures 77 and 10 K and helium gas density
0.18 mg cm−3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The combined efficiency of ion survival and transport as a function
of ionization rate density for different electric fields in the ionization region for temperature 10 K and helium gas densities 0.18 and
0.54 mg cm−3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The combined efficiency of ion survival and transport as a function
of the ratio of induced to applied voltage. . . . . . . . . . . . . . . . .
The combined efficiency of ion survival and transport as a function
of the relative recombination loss as calculated by Equation 5.3. . . .
Electric field profile along the ion transport trajectory. Electrode positions and the maximum voltages applied are marked on the top
axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic diagram of the electronics setup used for the mobility measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pulsing scheme used for the mobility measurement. . . . . . . . . . .
Transported ion intensity as a function of transport window width
measured for helium, neon and argon. . . . . . . . . . . . . . . . . . .
Measured reduced mobilities µred of 219 Rn ions in helium, neon and
argon gases as a function of the ratio E/N. The buffer gas densities
and temperatures used for the measurements are indicated in the
legend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cross-sectional view of the experimental cells used in experiments A
and B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic representation of the 219 Rn ion open source used in experiments A and B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Snowball efficiency as a function of electric field at 1.15K. . . . . . .
Snowball efficiency esb as a function of the inverse temperature 1/T.
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List of Figures
112
6.5
6.6
6.7
Total efficiency e f oil as a function of inverse temperature 1/T. . . . .
Extraction efficiency eextr as a function of inverse temperature 1/T. .
Snowball efficiency esb as a function of electric field E at the source
sat (1 − KE−2 ) is fitted to the data. .
for experiment A. The function esb
6.8 Extraction efficiency eextr as a function of inverse temperature 1/T.
The lines represent a constant plus an exponential function obtained
by fitting to the data points. . . . . . . . . . . . . . . . . . . . . . . . .
6.9 (a) Schematic side view of the bottom electrode incorporated with
the second sound heater and top view of the second sound heater.
(b) Photograph of the bottom electrode incorporated with the second
sound heater from the top. . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 Net evaporation mass flux as a function of the temperature variation
∆TW at the second sound wave front for the bulk helium temperatures 1.74 K and 2.04 K (from [47]). . . . . . . . . . . . . . . . . . . . .
6.11 Extraction efficiency eextr as a function of second sound pulse period
Pss for the temperatures 1.15 K and 1.60 K . . . . . . . . . . . . . . .
6.12 Snowball efficiency esb as a function of second sound pulse period
Pss for the temperatures 1.15 and 1.60 K. . . . . . . . . . . . . . . . .
. 82
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. 89
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