\begin{spacing}{0}
\chapter{Introduction}
\label{chap:introduction}
\end{spacing}
\
\par
Accelerator-based sources of exceptionally intense, tightly focused beams of X-rays and
ultraviolet radiation make possible both basic and applied research in fields from
physics to biology to technology that are not possible with more conventional equipment.
The development of a high-intensity source of muons can be useful for the production
of high-energy neutrino, thereby opening the door for a broad range of important new
physics experiments such as neutrino oscillation. The concept is to use a high-intensity proton beam
incident on a Hg jet to produce pions which decay to give the muons.
These muons is magnetically captured, accelerated, and then inserted into a storage ring.
\\

\section{Neutrino Factory for High Power Neutrino Beam}

\subsection{The concept of neutrino factory}

Accelerators are used to accelerate primary particle beams such as protons and electrons.
The required statistics in the collision processes demand a very high flux of primary particles.
On interaction of the primary particles with a target, it is possible to produce secondary beams
of elementary particles like pions, neutrons, and gammas. Primary protons pass through a linear
accelerator and further through a synchrotron, bunch compressors, and accumulators to achieve a
beam with a certain energy, intensity and beam structure. This beam is directed toward a target.
On interaction with the target, secondary particles of different kinds are produced.
A neutrino factory is the ultimate tool for producing a high-intensity neutrino beam to study
neutrino oscillations. The neutrino factory is based on a new concept of an accelerator
that produces a high-intensity, high-energy beam of muon and electron neutrinos.
It will allow an investigation of a new domain in neutrino physics such as
\begin{itemize}
  \item High intensity. Its flux is 10$^{3}$ times greater than conventional neutrino beams.
  \item High energy. It features a very high beam energy of 20 to 50~GeV.
  \item In a neutrino factory, the muon sign can be selected. Thus, it is possible to deliver particles and anti-particles.
\end{itemize}

The basic concept of the Neutrino Factory is the production of muon neutrinos and anti-electron
neutrinos from the decay of muons that are circulating in a storage ring.
An intense proton beam is delivered to a target, where pions are produced.
These pions are collected in a solenoid magnetic field, which can capture both
charged states of pions. The pions decay into muons in a decay channel.
The muon beam has both a large energy spread and transverse emittance.
The energy spread is reduced using a phase rotation, while emittance is improved by ionization cooling.
The cooled beam is accelerated to energies of 20 to 50~GeV and injected into a storage ring.

\subsection{Neutrino physics}

Muons cannot be produced directly, so pions have to be produced first. The first stage of a neutrino factory is thus a high-power proton driver that deliver protons onto a target, where pions are produced. These pions have to be collected and transported. After about 20~m, most of the pions decay into muons.
A neutrino beam can be produced from the decay of high-energy muons:

\begin{itemize}
  \item Pions from  Proton $+$ Material  $\longrightarrow \pi^{\pm} +$ X
  \item Muons from $ \pi^{\pm} \longrightarrow  \mu^{\pm} \nu_{\mu} (\overline{\nu_{\mu}}) $
  \item Neutrinos from $ \mu^{\pm} \longrightarrow e^{\pm} \overline{\nu_{\mu}} \nu_{e} (\nu_{\mu} \overline{\nu_{e}} ) $
\end{itemize}

At this stage, the muon beam has a low phase space density and resembles more a cloud than a beam.
Phase rotation as well as ionization cooling is applied to reduce the energy spread and the emittance of the muon beam.

Once the beam is cooled, it can be accelerated to a final energy of 20 to 50~GeV.
In the final stage of a neutrino factory, the accelerated muons are injected into a storage ring with long straight sections.

\section{A High Power Target for Neutrino Factory}

\subsection{Material consideration for a high power target}

The intensity of muon beam is directly proportional to the power of the proton beam which initiates the process. Considering that a high intensity proton beam is required in order to generate the required muons, the choice of the target material becomes a particularly important issue. Modeling studies point to high-Z materials
being more efficient at producing pions of both signs, whereas low-Z materials are better at preventing
the absorption of the produced pions \cite{Ozaki}.
The pion yield per proton increases with the atomic number of the target, as shown
in Fig.~\ref{fig:yield_material} from MARS calculation.
A high-Z material is desirable because the pion production cross-section increases with increasing Z. However, the intense proton beam would melt a target made of a solid high-Z material. A target system using a flowing stream of Hg could recycle the spent target. Several types of target material have been proposed including copper, graphite, and Hg.

Since these targets are envisaged as being stationary, one must consider the
problem of removing the energy deposited by the beam without interfering with the production of the particles.

\subsection{Moving metallic target for pion production}

While schemes for moving solid targets can be envisaged \cite{Thieberge},
a flowing liquid target is simpler, and Hg as a high Z material presents itself as the
liquid metal. The liquid target should be in the form of a free
jet, rather than being confined in containment, since the beam-induced
cavitation of the liquid metal can be destructive to solid
walls in the immediate vicinity of the interaction region. Another
issue associated with the proton beam is the effect of the energy
that it deposits in the target. The temperature of the target rises
almost instantaneously after the beam pulse, resulting in large internal
stresses that might crack a solid target or disperse a liquid target \cite{Kirk2001}. In the case of a liquid jet target, the dispersal of the jet by the beam should not
be destructive to the surrounding target system components and should not adversely affect pion
production during subsequent beam pulses, either on the microsecond
scale, if several micro-pulses are extracted from a proton
synchrotron, or on the scale of the macro-pulse period.
The operation of a liquid metal jet inside a strong magnetic field raises several magnetohydrodynamic issues such as possible deformation of the jet's shape and trajectory, as well as the effect
of the magnetic field on the beam-induced dispersal of the jet.

\subsection{Free mercury jet flow in a magnetic field for a high power target}

The free Hg jet in magnetic field is proposed for a high power target to overcome the issues
described in the above Chapter.
The concept is to use a high intensity proton beam incident on a Hg jet to produce pions which decay to give the muons \cite{Gabriel}.
The key elements of the target system are an intense proton source, Hg jet, and capture of
the generated pions in a high field solenoidal magnet \cite{McDonald2001}.
The schematics of the key elements of the target system is described in Fig.~\ref{fig:schem_jet_proton}.

Previous studies \cite{Ozaki} indicated that pion yield is maximized with a Hg target in the form
of a 1~cm diameter at the interacting center, tilted by about 150~milliradian with respect to the magnetic axis.
The target is tilted with respect to the axis of the capture solenoid, thus permitting the pions, whose trajectories are spirals, to leave the side of the target with a minimal probability for re-entering the target volume.
The pion yield per proton increases with the atomic number of the target, as shown
in Fig.~\ref{fig:yield_material} from MARS calculation. For 24~GeV protons, a
high-Z target is superior in yield.  As the pions emerge from the target at large
angles to the beam, and follow helical paths that may intersect the target at more
than one point, it is advantageous for the target to be in the form of a narrow
rod, tilted at a small angle to the magnetic axis. As shown in Fig.~\ref{fig:yield_jet},
suitable parameters for a Hg target are a tilt angle of 150~milliradian and a target radius
of 5~mm. However, jet motion in a magnetic induction field behaves differently, depending on the angle between the axis of the magnet and that of the jet, as a result of the differences in the magnitude of components of magnetic field \cite{Samulyak2006}. As the crossing angle increases, the transverse component of the magnetic field increases, but with no significant change in the longitudinal component. The increase in the transverse component of the magnetic field raises the induced current on the Hg jet. Therefore, the angle of the Hg jet is launched at 33~milliradian with
respect to the axis of the magnet, resulting in an interaction region about 30~cm long in case of a 1~cm diameter
Hg jet. Since the proton beam in TT2A beamline at CERN is horizontal, the Hg jet should make
a 34~milliradian angle with respect to the proton beam axis, and the magnetic axis should make an angle
of 67~milliradian with respect to the proton beam. The jet velocity is designed to be 15~m/s for the center
of jet to intersect the center of the proton beam at the center of magnet.

Based on the previous studies described in the above, the experimental setup parameters are determined.
The layout of experimental setup is more described below and optical diagnostic method for observation of
Hg flow in magnetic fields is more discussed in Chapter~\ref{chap:exp_method}.
Figure~\ref{fig:beam_jet_magnet} shows the detailed schematic of the overlap between key components of
the experiment. The velocity of the jet is 15~m/s, where the trajectory of Hg jet overlaps with the proton beam over 30~cm. The facility is a closed piping loop, constructed primarily of 316 stainless steel, and designed to circulate liquid Hg. The parameters of the proton beam and solenoid system are determined by the required conditions of particle production rates \cite{Bennett}.
Basic system parameters consist of proton energy 24~GeV, 14~GeV, and number of protons in one
pulse $\approx$ 3 $\times$ 10$^{13}$, which was extracted from the CERN(European Organization
for Nuclear Research) PS(Proton  Synchrotron) in 2007.
The solenoid length is 100~cm, inside radius is 7.5~cm, and a maximum magnetic field is 15~T. The solenoid magnet is titled at 67~milliradian angle with respect to the beam. The beam arrives at an angle 34~milliradian with respect to the jet which has a radius $\approx$ 0.5~cm, as schematically shown in Fig.~\ref{fig:beam_jet_magnet}. The angle between moving Hg jet and magnetic axis induces currents, which generates Lorentz force with
a component of magnetic field. Thus, it is expected that the optimal 150~milliradian of jet axis with respect
to magnetic axis distorts jet shape \cite{Gallardo2002}.
Therefore, 33~milliradian of jet axis with respect to magnetic axis was designed for experiment to yield
minimum distortion of jet shape.
The 24~GeV proton beam is directed on to the solenoid at 67~milliradian off the solenoid axis, so that most high momentum particles do not travel straight down the beam line \cite{Gallardo2001}.
If there are no magnetic and gravitational effects on the Hg jet trajectory, the beam should enter at the bottom surface of Hg jet at Viewport 1, which is located
at approximately 30~cm from the nozzle and the beam should exit on the top surface of Hg jet
at Viewport 3, which is located at approximately 60~cm from the nozzle.
The required jet velocity is determined by two conditions: 1), the need to replenish the
target before the arrival of subsequent proton beam pulse, and 2), it should be high
enough to overcome the deceleration force induced by Lorentz force \cite{Hassanein2001}.

Initial tests were performed at the BNL Alternating Gradient Synchrotron (AGS) \cite{Kirk2001}, and
continued at the CERN ISOLDE facility \cite{Lettry}. The BNL test featured a 24~GeV proton beam
interacting with a free Hg jet with a nozzle diameter of 1~cm and a velocity of 2.5~m/s.
The delivered proton bunch was focused to $<$1~mm radius, resulting in a peak
energy deposition of 80~J/g, delivering 24~GeV proton beam at 15~Hz \cite{Tsoupas}.
These initial tests did not have a magnetic field on the target. A parallel effort was
undertaken to study the effects of high velocity Hg jets in the
presence of high-magnetic fields, but with no proton beam \cite{Fabich}.

\subsection{Impact of the MHD mercury jet experiment for an intense proton target}

The previous experiments did not perform the Hg jet in a high magnetic field interacting with an
intense proton beam. In this work, we integrated the Hg jet, solenoid magnet, and intense proton
beam all together.
The performance and feasibility of utilizing liquid metal jet as a target for an intense proton beam is explored experimentally, which is an explicit objective of the experiment.
The liquid jet target concept is recyclability otherwise the target would be destroyed.
Therefore, the power of the target has to be evaluated in terms of the replacing capability
and validated experimentally. In order to validate the performance of the target, the MHD jet
behavior in a strong magnetic field has to be investigated. The response of the Hg jet
due to the energy deposition by interacting with an intense proton beam has to be studied
and the magnetic field effect to the disruption of Hg jet has to be studied, as well.
The experimental results reveals that the effect of the Lorentz force to the jet stabilization
as well as the deflection of jet. The experimental results provide feasibility of utilizing liquid metal jet
as a target for an intense proton beam.

\section{Mercury Target Issues}

\subsection{Mercury jet disruption by energy deposition from an intense proton beam}

The production of large fluxes of particles using high energy, high intensity proton pulses impinging on
solid or liquid targets presents unique problems which have not yet been entirely solved.
The large amount of power deposition required in the material coupled with the short pulse duration
produce large, almost instantaneous local heating.
The interaction of the proton beam with the Hg target leads to very high heating rates in the target,
where the heat from the beam could melt or crack a high-Z target.
Sudden energy deposition into Hg jet causes increase in temperature by specific heat capacity.
Increase in temperature causes volumetric changes by the volumetric thermal expansion coefficient,
which results in pressure rise analogous Young's Modulus relationship between stress and strain.
Thus, strain energy is built up in the Hg jet. This strain energy is released as kinetic energy
such as filaments development on jet surface.
The resulting sudden thermal expansion can result in damage causing stresses
in solids and in the violent disruption of liquid jets. The volume expansion initiates vibrations
in the material. The amplitude of these vibrations is such that stresses that exceed the strength of
the material can be generated, causing mechanical failure \cite{Thieberge}.

\subsection{Magnetohydrodynamic issues in mercury jet target}

Liquid metal jets are proposed as potential target candidates because the heat energy can be removed along with the moving liquid. For Hg, heat conduction is very effective compared to convection: thermal diffusivity is
dominant. In heat transfer, the Prandtl number indicates the relative thickness of the momentum and thermal
boundary layers. When Prandtl number is small such as Hg, it means the heat diffuses very quickly compared
to the velocity. However, there are two important problems that are associated with the use of
liquid metal targets in these environments. First, as the liquid jet penetrates the magnetic field, instabilities in jet motion and deceleration may occur because of the large field gradients at the entrance and exit of the solenoid. The designed jet velocity is $\sim$ 15~m/s $\sim$ 20~m/s,considering the repetition rate of
target and avoidance of bending jet trajectory in order to have 2 interaction length between proton beam
and jet. Theses instabilities may change the jet shape into one that is significantly less efficient
for pion production \cite{Hassanein2001}.
Second, during the intense pulse of energy deposition in a short time, the resultant stress could break up the target, where the liquid jet can develop surface instabilities such as filaments after beam interaction.
These filaments may damage to surrounding facility under operation of target because of similar
characteristics of Hg to metal.

Hg flow in a magnetic field experiences induced currents, which causes the jet to produce
transverse forces normal to jet axis direction resulting deflection normal to jet axis \cite{Gallardo2001, Gallardo2002}. In addition, axial currents are induced if the jet axis does not coincide with the magnetic
field axis. These axial currents produce elliptical distortions of the Hg jet.
Faraday's law can be used to obtain the azimuthal current density from changing the axial field
in the local coordinate system of the Hg jet.
The transverse component of the magnetic field normal to the jet axis also varies along the trajectory of the Hg jet. The axial current density can be related to the changing transverse component of
the magnetic field normal to the jet axis. These axial currents produce a magnetic force. This force will be balanced by a restoring force from the surface tension of the Hg, and with the condition that the Hg is an incompressible liquid, will produce an elliptic deformation of the Hg jet \cite{Oshima}.

\subsection{Overview of experimental investigation of MHD flow and discussion}

A proof-of-principle experiment performed at the CERN(European Organization for Nuclear Research)
PS(Proton Synchrotron), which combined a free Hg jet target with a 15~T solenoid magnet
and a 24~GeV primary proton beam. \cite{Bennett}.
The disruption of jet could be much longer than beam-jet interaction length,
which must be investigated experimentally and a key purpose of experiment.
The experiment validates the liquid type of target for producing
an intense secondary source of muons by showing the jet repetition rate to replace the disrupted
target by the energy deposition from an intense proton beam. Also, due to the energy deposition in jet by
an interaction of proton beam, the filaments development on jet surface could damage and eventually
break the facility of surrounding wall. The filament velocity could be much high, which must be
investigated experimentally and another key purpose of experiment.
For the investigation of feasibility, various behavior of Hg jet
in magnetic fields interacting with proton beam is reported based on experimental measurement.

The PS runs in a harmonic 16 mode and can fill up to 2 $\times$ 10$^{12}$ protons/bunch (2~Tp/bunch), where
the term ``harmonic" means sinusoidal pulse shape, the term ``8(16)" means number of bunches, and
the term ``bunch" means sub-pulse in a pulse. Note that Tp(Tera protons) means 1 $\times$ 10$^{12}$ protons.
This allows up to 30 $\times$ 10$^{12}$ protons per pulse on the Hg target,
generating a peak energy deposition of $\sim $ 130~J/g with $\sim$ beam spot size of 5.7~mm$^{2}$ at beam
energy 24~GeV, which is a key design parameter of single pulse at CERN for a target system capable
of supporting proton beam with powers of 4~MW. Note that CERN could provide requirement of this key design parameter.
For this experiment, a solenoid with a bore of 15~cm for a high magnetic field was designed.
This magnet is capable of delivering a pulsed peak field of 15~T \cite{Titus}.
The pulsed solenoid incorporates a magnetic field ramp up of 9~seconds and
is capable of sustaining its peak field for a duration of $\sim$ 1~second.
The magnetic axis is positioned at an angle of 67~milliradian with respect to the proton beam, with the tilt
provided by a common baseplate supporting all the equipment.
The relationship between the measured magnetic field and the applied solenoid current was mapped to
deduce the maximum magnetic field at the center of the solenoid \cite{Titus}.
A 5.5~MW, 700~V power supply delivers 7500~A of current to pulse the solenoid \cite{Michael, Martins, Kirk20082}.
Figure~\ref{fig:magnet_operation} (a) and (b) show the the estimated jet velocity in nozzle during Hg
loop system operation and the calculated behavior of the 15~T magnet during a pulse \cite{Graves20072, Kirk20082}.
Approximately 30~MJ of energy is dissipated in the magnet, which raises its temperature
from 80 to 120~K. Note that CERN could provide requirement of this key component for experiment.
The magnet is cryogenically cooled by liquid nitrogen to
77~K prior to operation and warms up by 30~K during pulsing due to 30~MJ coil heating \cite{Haug}.
Figure~\ref{fig:cryostat_process} shows cryogenic process of cooling 15~T solenoid magnet.
Therefore, a 30~minute cooling time is needed for each single shot. The
magnetic axis is positioned at an angle of 67~milliradian with respect to
the proton beam, with the tilt provided by a common baseplate supporting
all the equipment (see Fig.~\ref{fig:loopmagnet}(a)). It was found that the maximum magnetic
field reached 15~T at Plasma Science and Fusion Center in Massachusetts Institute of Technology \cite{Titus}.

The Hg jet delivery system generates a Hg jet from 1~cm diameter nozzle with velocities
up to 15~m/s \cite{Graves20071}. The primary diagnostic of the beam-jet interaction is optical.
A set of four view-ports along the interaction region is connected by imaging fiber-optic bundles to
four high speed cameras.
The cross-section and actual equipment for the Hg system with high field solenoid magnet is shown in Fig.~\ref{fig:loopmagnet}. The horizontal line in Fig.~\ref{fig:loopmagnet}(a) represents the proton beam. The Hg jet, which is ejected from right to left in Fig.~\ref{fig:loopmagnet}(a), co-propagates with the proton beam. Four Viewports are shown within the solenoid bore, which represent viewing locations for observation of the Hg jet within its primary containment vessel.
The Hg system provides for double containment vessel of the hazardous liquid metal, and can be inserted or removed from the solenoid bore without disassembly. Figure~\ref{fig:schem_hydraulic} shows schematics of
Hg loop system for experiment. A hydraulic syringe pump, with a piston velocity of 3~cm/s was used to
pulse the Hg jet. This pump minimizes the heat added to Hg as opposed to a centrifugal pump. The syringe
pump also reduces the discharge pressure which is the limitation of a centrifugal pump. The Hg system provides a jet duration of a $\sim$ 3~seconds of constant velocity profile. A total of 180~kg of Hg is loaded in the
system. A 30~kW, 200~bar hydraulic power unit drives the syringe pump \cite{Graves20072}.

Each pulse of the proton beam delivered to this system constitutes a separate experiment.
About 360 beam pulses are utilized in a beam-on-demand mode at CERN.
These pulses span a range of intensities and time intervals between the multiple extracted bunches
per pulse. The magnet operates over a range of field strengths of 0 $\sim$ 15~T.

In Chapter~\ref{chap:mhd_math}, the full MHD governing equation using Maxwell's equations are
presented. Governing equations of conducting flow in a magnetic field are formed, where the
contribution of Lorentz force to the hydrodynamic equations is discussed.
The reviewed equations are employed in Frontier MHD code, whose results are referenced for comparison with
experimental results.

In Chapter~\ref{chap:exp_method}, the detailed layout of optical diagnostic setup and its installation are
presented. The design of each key component for the experiment is presented.
As a primary diagnostics, the scientific development of optical diagnostics employing the high
speed cameras and infrared lasers to freeze the transient motion of Hg jet is presented and
the performance of the scientific instrument as well as the methodology to capture images are discussed.

In Chapter~\ref{chap:exp_result_mhd}, ~\ref{chap:exp_result_beam}, and ~\ref{chap:exp_result_velocity}, MHD behavior of Hg jet in various magnetic fields is discussed based on the observation from experiment.
Also, the characteristics of Hg jet in magnetic fields interacting with an intense proton beam
are presented, where the effect of magnetic field to suppress of disruption of jet and reducing of
filament velocity are investigated to validate the performance and feasibility of utilizing Hg jet
as a high power target. The key result to validate the feasibility of the high-Z liquid target is
addressed based on the experimental measurements and the beam pulse structures.

To conclude, discussion based on understanding of MHD flow from various literatures and experimental results
is summarized in Chapter~\ref{chap:conclusions}.

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  \includegraphics[width=6in]{yield_material4}\\
  \caption{Pion yield versus atomic mass number of target at three proton beam energies \cite{Ozaki}.}
  \label{fig:yield_material}
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\includegraphics[width=6in]{schem_jet_proton2}
\caption{Geometry of key elements of target system and Viewports, showing the overlap between the Hg jet, magnetic axis, and the proton beam. a.) Top view. b.) Side view. } \label{fig:schem_jet_proton}
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  \includegraphics{yield_jet}\\
  \caption{Pion yield from Hg target versus tilt angle between the target/beam axis and the solenoid axis and versus the radius of the target \cite{Ozaki, Mokhov2001}. a.) Pion yield versus target radius. b.) Pion yield versus tilt angle.}
  \label{fig:yield_jet}
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  \caption{Schematics of the relative overlap between proton beam axis, Hg jet axis , and solenoid magnet axis. Viewport1, Viewport2, Viewport3, and Viewport4 are located 30~cm, 45~cm, 60~cm, 90~cm apart from nozzle exit, respectively.}
  \label{fig:beam_jet_magnet}
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\caption{Operation of Hg loop system and pulsed 15~T solenoid magnet. a.) Hg loop system command \cite{Graves20071}. b.) Behavior of the 15~T solenoid magnet during a pulse \cite{Kirk20082}.} \label{fig:magnet_operation}
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\caption{Cryogenic process of cooling 15~T solenoid magnet \cite{Haug}. a.) Cooling of proximity cryogenics.
b.) Magnet cooldown. c.) Magnet at 80~K. d.) Emptying of the magnet cryostat. e.) Magnet pulse. f.)
Re-cooling of magnet. } \label{fig:cryostat_process}
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\caption{Photographs of the entire MERIT(Mercury Intense Target) experiment \cite{Graves20072}. a.) Sectional side view of Hg loop system integrated with 15~T solenoid magnet. b.) Fabricated Hg loop system assembled with 15~T solenoid magnet (Top view). } \label{fig:loopmagnet}
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\caption{Schematics of Hg loop system for MERIT(Mercury Intense Target) experiment \cite{Graves20072}.} \label{fig:schem_hydraulic}
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