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\chapter{Conclusions}
\label{chap:conclusions}
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\par

\section{Mercury Intense Target Experiment}

This experiment is a proof-of-principle test for a high-Z target system capable
of accepting a high intensity 4~MW proton beam. The system allows
for the production of copious pions which subsequently decay into muons.
An experiment at the CERN proton synchrotron that combines a free Hg jet target with a
15~T solenoid magnet with 14~GeV and 24~GeV proton beam was performed. It validates
the liquid type of target concept for production of an intense secondary source of muons.
When interacted with a beam pulse of 30 $ \times$ 10$^{12}$ protons on the Hg target,
this generates a peak energy deposition of $\sim$ 125~J/g, which leads to the disruption of Hg target.
For this experiment, a 15~T pulsed solenoid was designed.
The Hg jet loop system generates a Hg jet from 1~cm diameter nozzle with velocity 15~m/s.
An optical diagnostic system based on back-illuminated laser shadow photography is employed to investigate the Hg jet flow. Synchronized short laser light pulses are used to illuminate and freeze the motion of the jet. A total of four optical imaging heads for each Viewport are mounted on the exterior of the primary
containment vessel. Four high speed cameras are used to simultaneously collect images on four Viewports.
Integrated all-in-one compact optical heads, consisting of ball lens, illumination fiber, objective lens, and imaging fiber bundle, are placed at the radius of curvature of a retro-reflector allowing for the illumination and imaging collection on one side of the Hg primary containment vessel.
Due to the short time of frame rate, the time delay between illumination of the light source and captured
image at camera CCD is adjusted, which is judged by the uniformity of consecutive collected image brightness
as well as the triggering signal pulse on the oscilloscope for each component of device, so that timing of
transient motion of jet interacting with proton beam could be validated.
In experiment, the fiber optics coupled diagnostic system played an principal diagnostic role in providing
Hg jet target behavior interacting intense proton beam in a high magnetic field.
The optical diagnostic system in design requirement had space limited restriction and ultimate environment
such as high magnetic field and high radiation area since it was placed in the center of high magnetic field of solenoid right next to the beam-jet interaction. However, no significant image distortion and no change in the functions of instruments including remote control were observed under such a restricted environment during experiment.

\section{Mercury Jet in a Magnetic Field}

In order to understand a conducting flow in a magnetic field,
MHD equations considering Lorentz force effect based on the Navier-Stokes
equations and Maxwell equations are reviewed. The suppression of vorticity by
the perpendicular magnetic field is reported based on the role of Stuart number.
As a result, the rotational motion of jet on the surface becomes more two dimensional motion of
flow and thus the jet surface is more stabilized, which is observed qualitatively.
The energy deposition mechanism by a sudden interaction of proton beam are reviewed by employing energy of state,
where the formation of cavities is believed to take place and the cavitation bubbles influence the wave
dynamics in Hg. Two phase equation of state is reported to consider the pressure change by energy deposition
of proton beam, leading to the breakup of jet and generation of filaments on Hg jet surface.
The role of magnetic damping and global energy equations are reviewed, where the global kinetic
energy declines exponentially on a time scale of magnetic damping constant if the flow velocity is
perpendicular to the applied magnetic field. The phenomenology of magnetic damping explains the
decrease of filament velocity as a function of time in a magnetic field.

The motion of Hg jet at Viewport 1 $\sim$ 4 enabled us to understand Hg jet condition at upstream, midstream,
and downstream. Image processing provides the Hg jet size in various magnetic fields.
Optical diagnostic observation showed the effects of the magnetic field on the distortion of Hg jet
induced by axial current along jet axis interacting with transverse magnetic field generated by the angle of
jet axis with respect to the magnetic field axis, generating Lorentz force, which is possibly the onset
of a quadrupole effect at larger than 10~T. The jet size becomes larger at larger magnetic field than 10~T.
The comparison of measurement with numerical calculation using Frontier MHD code showed somewhat
consistency between 10~T and 15~T, but the experiment observed the nature of diverging turbulent jet.
Nevertheless, the stabilizing effect of the magnetic field on turbulent Hg jet is observed.
The wave length on the jet surface increases as magnetic field increases. Thus, the jet surface is
getting flattened. Therefore, the jet is getting more stabilized.
The experimental results clearly show that the magnetic field
stabilizes the Hg jet by reducing the amount of fluctuations on jet surface and smoothing out
the edges of the otherwise turbulent Hg flow, as previously reported in the
literatures \cite{Bernshtam, Gold, Kozyrev, Shercliff1956} and predicted in Frontier MHD simulation.
Gravity affected the Hg jet trajectory, so that the Hg jet bended down at downstream.
But this deflection of the Hg jet by gravity is reduced at higher magnetic field.
The jet axis becomes more straight toward the direction of magnetic field line.
The global fit of measured position of jet centroid approximated the Hg jet flow trajectory in a
magnetic field, which enabled us to check the position of nozzle and launching velocity of Hg jet at nozzle.

It is reported that the transverse magnetic field drops pressure of flow, resulting decrease the flow velocity and change of velocity profile, so called Hartmann flow.
However, it was observed that the longitudinal jet velocity was not changed in $\sim$ 15~T of longitudinal magnetic field. This can be deduced from Lorentz force equation, where the flow velocity and magnetic field are cross product. This result reinforces the assumption of the Hg jet shape in a magnetic field to be elliptic.
The pressure at pipe inlet driven by the syringe piston is measured. The Hg driving pressure
was same independent of the magnetic field. Therefore, the Hg flow was not influenced by
the longitudinal magnetic field. However, pressure head losses by pipe geometry are investigated.
Friction of inside pipe was contributed mainly among several head losses.
According to the velocity measurement at upstream, mid-stream, and downstream, it was not significantly
changing, but same comparable to that at 0~T. Therefore, the magnetic field effect at the pipe bend is
expected to be somewhat negligible, but possibly some discharging loss from nozzle may contribute to
reduction of flow velocity.

The comprehensive optical diagnostics allowed us to have a better understanding of the behavior of a
conducting jet moving in a high magnetic field environment up to 15~T with jet velocity 15~m/s.

\section{Disruption of Hg Jet and Filament on Jet Surface in a Magnetic Field}

Proton beam spot size by optics is estimated by measuring dispersion and emittance of beam.
Also, measurement of beam spot size by camera screen monitor is performed, which showed 2 times
larger than that by optics. The beam spot size scales with beam intensity.

Numerical Monte Carlo simulation was performed at FNAL by collaborator for calculation of energy deposition 
into Hg jet, where the jet size, trajectory, and proton beam spot size from measurement and magnetic field,
beam intensity, and beam energy were input. The jet shape was assumed to be elliptic based
on observation and measurement of jet size and flow velocity.
The peak energy deposition as well as total energy deposition into Hg jet were calculated.
Multi-variable fit provides the relation of peak energy deposition and total energy deposition
with beam intensity, beam energy, and magnetic field. Also, the mass weighted averaged energy
deposition shows the distribution of energy along jet axis as well as the influence of beam intensity
and magnetic field. Since the beam spot size increases with beam intensity, the peak
energy deposition decreases with beam intensity, appearing to be parabolically decreasing. 
However, the total energy deposition into Hg jet was not significantly changed with beam intensity,
which approximated to be $\sim$ 6 $\sim$ 8 $\%$ of the incident beam energy.

The observation of interaction of proton beam up to 30~Tp at both 14~GeV and 24~GeV beam with
15~m/s jet was performed, which provided key results to validate the performance of high power target.
The disruption as manifested by the jet break up is caused by energy deposition of proton beam.
The disruption typically starts at the bottom surface of Hg jet where the proton beam enters.
The disruption typically ends at the top surface of Hg jet where the proton beam leaves.
The jet breakup is observed typically at center of jet flow where the maximum energy is deposited.
This phenomenon is consistent with the beam trajectory across the jet and the result of
energy deposition distribution calculated by MARS code, as well.
Based on the threshold of beam intensity causing the disruption of Hg jet in various magnetic fields,
the extent of length of disruption over the entire jet is estimated using the calculated distribution
of energy deposition, which gives somewhat agreement with experimentally measured disruption length.
A proton beam pulse is composed of 8 and 16 bunches with a doubled bunch period.
The effect of pulse structure on disruption length is negligible, which means that
the instantaneous time incident to Hg jet by beam does not affect to difference of
energy deposition into Hg jet.
From the parameterized fit to total energy deposition, peak energy deposition, and fluence,
the energy deposition into Hg jet according to beam intensity, beam energy,
and magnetic field is estimated, which provides an extrapolated estimation up to 25 T.
The threshold of disruption increases in $\sim $ 0.8 power of magnetic field, and it is $\sim$ 338~J
of total energy deposition with no magnetic field. Also, the threshold of disruption is
$\sim$ 10~J of peak energy deposition with no magnetic field, and it increases in 1.2 power of
magnetic field. The disruption length increases in square root power of total energy deposition
with no magnetic field, but it is suppressed in $\sim  \ 1/(2 + 0.04 B)$ power of total energy
deposition with magnetic field.

The time scale of magnetic damping indicates the rate of decay of global kinetic energy due to
the magnetic field.
Therefore, the rising time to peak velocity increases as the magnetic field increases, which
corresponds to the transient response time as an indication of magnetic damping.
At low intensity of proton beam, the charged beam may be fluctuating depending on the initial
conditions at experiment. Thus, the observed onset time of filament was scattered much at low intensity of
beam and it decreases as the intensity of proton beam increases.
Therefore, the distribution of filament velocity at lower intensity of beam is more scattered.
The effect of geometry of viewing filament is observed. The onset time of 
filament decreases as the uniformly distributed filament velocity on jet surface increases.
The maximum observed filament velocity scales with beam intensity due to the increased energy
deposition, but the magnetic field slows the maximum observed filament velocity.

From the parameterized fit to peak energy deposition and total energy deposition,
the energy deposition into Hg jet according to beam intensity, beam energy,
and magnetic field is estimated, which provides an extrapolated estimation up to 25~T.
Measurement from multiple events with repetition under same condition using pump-probe shot showed
somewhat good agreement with disruption length results and provided possible error value for
deviation occurred by repeating experiment under same condition.
The threshold of filament velocity increases in 1.2 power of magnetic field.
The filament velocity increases in linear ($\sim$ 1.24) power of peak energy deposition
with no magnetic field, but it is slowed in $\sim  \ 1.24 - 0.015 B$ power of peak energy deposition with magnetic field. Comparison of filament velocity with numerical simulation was performed as a check.
The effect of geometry of viewing filaments were considered and the measurement showed somewhat lower
than that in simulation due to the magnetic field effect and uncertainty of estimated location of filament
for consideration of geometry of viewing filament.

Based on the measured data from observation of image and energy deposition estimated by elliptic 
jet model in MARS code, various global fit provided estimation of the key results and statistic 
approach such as $\chi^{2}$ probability provided quality of the goodness of fit.
Thus, the various investigations from the analysis of Hg jet motion in a magnetic field and the analysis of 
disruption length and filament velocity were able to be integrated for providing the basis of
forming the conclusion of the experiment.

\section{Feasibility of High-Z Target for Future Particle Acceleration}

The performance and feasibility of utilizing liquid metal jet as a high power target was investigated.
The liquid jet target concept is based on the target being recycled after each pulse.
Therefore, the power of the target is evaluated in terms of the replacing capability.
The optimal interaction length for the 24~GeV beam energy is in the region of 30~cm which
corresponds to approximately 2 interaction length for Hg. For a 20~m/s jet velocity, replacing
two interaction lengths will be taken in 14~ms thus allowing for operations with a repetition rate
of up to 70~Hz.  The disruption length at 15~T is less than 20~cm and the total energy deposition
is $\sim$ 8000~J. Therefore, 100 $\sim$ 133~kJ of beam energy can be recycled with a 70~Hz repetition
rate for 20~m/s jet. This result validates that a target system capable of supporting proton beams
with powers of up to 8~MW, which concludes the experiment for investigation of feasibility of Hg jet as
a high power target.


