Nuclear Instruments and Methods in Physics Research A 503 (2003) 336–339
Experimental observation of proton-induced shocks and
magneto-fluid-dynamics in liquid metal
A. Fabich*, J. Lettry
CERN, CH-1211 Geneva 23, Switzerland
Abstract
A liquid metal target is one of the options for the pion production target of a n-factory. The interaction between a
liquid metal and a proton beam were observed with static mercury as well as with a free mercury jet and up to 4 1012
protons/bunch. The experimental method for investigating the magneto-fluid-dynamic effects of a high-velocity liquid
metal in a high magnetic field magnet has been validated by recording the behaviour of a 15 m=s mercury burst entering
the gradient of a 13 T solenoid at GHMFL Grenoble.
The paper includes the description of the optical read-out system as well as numerical results of the mercury drop
velocities.
r 2003 Elsevier Science B.V. All rights reserved.
PACS: 47.65.+a; 29.25.Pj
Keywords: Target; High power; Mercury; MFD; Neutrino factory
1. Introduction
The liquid metal target is a natural solution to
the stresses and fatigue, induced by the proton
beam, that eventually lead to the destruction of
most solid targets. A liquid jet would provide a
new target for each proton pulse if the material
disrupted by the proton beam can be evacuated
within the proton pulse interval. To study the
interaction of a liquid metal with a proton beam a
static mercury target and a mercury jet with free
surface have been exposed to a proton beam
ð24 GeV; 150 ns) at the AGS, BNL (experiment
E951). Mercury was chosen as one of the room*Corresponding author.
E-mail address: [email protected] (A. Fabich).
temperature liquid metals. Its high density reduces
the physical length of the target and influences the
design of the pion capture system, the spread in
time of the resulting p-burst, and the absolute pion
production [1]. For the pion capture system, in the
environment of the target, two scenarios are
proposed. The CERN community is presently
going for a magnetic horn scheme. The US
scenario includes a 20 T solenoid with injection
of liquid metal into a high magnetic field. The
experimental setups are based on the recording of
the shadow of the mercury, intercepting a laser
light source, with a high-speed camera. Sets of
mirrors and telescopes allow the installation of the
sensitive pieces of electronics out of the magnetic
field or behind a few meters-thick radiation
shielding.
0168-9002/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0168-9002(03)00710-1
A. Fabich, J. Lettry / Nuclear Instruments and Methods in Physics Research A 503 (2003) 336–339
2. Interaction of the mercury target with a proton
beam
2.1. Experimental setup
Thimble: The thimble experiment provides a
simple setup to study the phenomena at proton
impact on liquid targets. The amount of mercury,
which is irradiated, is by far smaller, as no spare
material for circulation is needed. As experiments
for both setups under the same conditions were
performed, the results can be compared against
each other, and future experiments with a thimble
can bring up results which can be scaled to the case
of a free jet target. The volume of the thimble
excavated in a stainless-steel frame is 1:2 cm3 : It
consists from bottom to top of a half-sphere ðr ¼
6 mmÞ; a vertical cylinder ðr ¼ h ¼ 6 mmÞ; and a
meniscus, which has a free surface of 1:2 cm2 :
Jet: The continuous jet was ejected from a
cylindrical nozzle (diameter 1 cm) under an angle
of 14:5 from the horizontal plane and followed by
a parabolic line. The view of the camera, which
covered a round area with a diameter of about
8 cm; was centred on the zenith of the jet. With the
beam centre line at the zenith of the jet a total
physical intersection of jet and beam is given along
a distance of 19 cm: In total, 12 proton pulse
impacts on jet and target have been performed.
The main parameter of the beam is the proton
intensity, which was varied from 1–4 TP:1 The
effects of the parameters ‘beam spot size’ and
‘bunch length’ cannot be determined due to low
statistics. The information of the spot size was
measured with an alumina foil ðrr:m:s: ¼ 1:5 mm 1 mm; horizontal/vertical).
Measured quantities as a function of the proton
intensity per pulse are the explosion velocity and
disruption length and offset. The disruption length
and its offset relative to the zenith are only
measurable in the jet setup, as there is no
equivalent in the case of the thimble.
Temperature profile: The temperature distribution within the target has been simulated for the
two experiments using MARS [2]. Assuming a
proton pulse with an intensity of 4 TP and a spot
1
1 TP ¼ 1012 protons:
337
size radius of 1 mm (r.m.s.) the main characteristics are an average temperature rise in the target
centre of 200 K for the thimble and 300 K for the
jet target. The radial distribution is a parabolic
slope down to Zero at the boundary of the target.
The average temperature rise is 57 K (thimble) and
65 K (jet). The two temperature distributions are
very similar, in the case of the jet the shower is
more developed as the target length ðl ¼ 19 cmÞ is
about 1.5 interaction lengths.
2.2. Velocity measurements
The velocities measured from the movies of the
thimble and jet splashes are plotted in Fig. 1. The
data points represent drop sizes greater than 1 mm
as a result of our resolution. A small fraction of
the jet is dispersed into small, fast droplets. The
larger part ðE80%Þ is not accelerated that high.
The upper limit of the dominating velocity is
indicated by the solid line. The errors of the
shutter time ðt ¼ 25 msÞ and the spatial resolution
ð0:89 mm=pixelÞ result in an error of the velocity
measurement of 5%.
Fig. 1. Droplet velocities measured over a typical distance of
2 cm for the thimble (triangle) and the jet (circles). The solid
line shows the upper limit of the dominating velocities (jet).
Also indicated is the theoretical velocity according to Ref. [3]
for the jet (dashed line). The theoretical velocity for the thimble
is about 30% below the one of the jet due to the lower
temperature rise.
338
A. Fabich, J. Lettry / Nuclear Instruments and Methods in Physics Research A 503 (2003) 336–339
Assuming the model given in Ref. [3], the
explosion velocity v is estimated as the ratio of
thermal expansion by the time the sound wave
needs to travel to the boundary of the mercury
target and is given by v ¼ 0:25aV DT0 c; where aV is
the volume expansion coefficient, DT0 the temperature rise on the centre axis, and c the velocity
of sound in the medium. These predicted velocities
for the jet are indicated in Fig. 1 and agree nicely
with the measurements.
2.3. Disruption length of the jet
An interesting number, to decide between a
pulsed or continuous jet as a target, is the length
for which the jet is disrupted. As the jet passes the
viewing area of the camera, the extension of the
destructive interaction between the p-beam and
the mercury jet can be determined by computing
the origin of the Hg drops. From this it can be
learned whether a destructive pressure wave is
travelling along the mercury jet outside the initial
geometrical intersection region. Fig. 2 is a scattered plot of the disruption length and position as
a function of the distance along the jet and the
proton intensity. Fig. 3 shows a projection of
Fig. 2 on the position axis, where the ordinate
shows the number of entries, which is proportional
Fig. 2. Disruption length and its position along the jet for all
eight pulses at different proton intensities. The dashed line
indicates the invisible disruption for the event at 3:8 TP; where
the disruption is extended to outside the viewing area.
Fig. 3. Probability of jet rupture and its Gaussian fit. The two
bars indicate the viewing length of the jet (black) and the
physical intersection region of jet and beam (pattern). For an
4 TP-proton impact the temperature rise on axis along the jet is
shown (dashed). Proton beam and mercury-jet ðv ¼ 2:5 m=sÞ
arrive from the right.
to the probability of rupture of the jet. We
observed no rupture outside the geometrical
intersection region and therefore support a continuous jet target option.
3. Magneto-Fluid Dynamics
A magnetic horn [4] and a 20 T solenoid [1] are
proposed for the pion capture system for Neutrino
factories. Using a mercury jet as a target, a liquid
metal is injected into a magnetic field and
magneto-fluid-dynamic (MFD) effects occur.
In spring 2001 an experimental setup has been
tested at the Grenoble High Magnetic Field
Laboratory (GHMFL). A mercury jet of a
diameter of d ¼ 3 mm has been injected into
vertical solenoid ðBmax ¼ 13 T; ð@B=@zÞmax ¼
65 T=m; dbore ¼ 12 cmÞ with a velocity of up to
v ¼ 15 m=s:
On injecting a mercury jet into a magnetic field,
a repulsive force acted on the tip of the mercury
jet. This resulted in a shaping of the mercury tip
towards a shape similar to the tip of a rocket. The
MFD effects observed during the on-axis injection
were qualitatively predicted [5] and confirmed the
sensitivity of the measurements.
A. Fabich, J. Lettry / Nuclear Instruments and Methods in Physics Research A 503 (2003) 336–339
4. Conclusion
*
*
*
*
The mercury thimble and jet experiments
confirmed reasonably the predictions for the
behaviour of a liquid metal target at the impact
of a proton pulse. The thimble provides a
simple setup for studying proton-induced
shocks.
Dominating velocities measured were up to
10 m=s and the maximum velocity of up to
45 m=s for a bunch intensity of 4 1012
protons.
The rupture of the mercury jet outside the
intersection of jet and beam did not occur,
which makes the use of pulsed target jets
unnecessary.
The MFD measurement setup is validated and
showed quantitatively the expected effects.
Acknowledgements
We would like to thank our colleagues from the
E951 collaboration at BNL, the CERN horn and
targetry group and the staff of GHMFL in
Grenoble for their great support.
339
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