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«STUDENT RESEARCH PAPERS SUMMER 2011 VOLUME 22 REU DIRECTOR UMESH GARG, PH.D. REU Student Research Papers – Summer 2011 University of Notre Dame – ...»

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Loop timer The loop timer function begins timing in milliseconds upon being called and continues timing throughout the duration of the program. When entering a new loop the loop timer continues to count but will not display the counting change in the new loop. This means a loop timer in a previous loop will only display the time at the start of the new loop on an indicator in the new loop. When using multiple loop timers, once the first loop timer is called all future loop timers also begin timing. This timing function only keeps track of the amount of milliseconds after it was called and does not work for determining the time of the day.

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St. George Dipole Magnets The six dipole magnets on the St. George will be water cooled to 55 degrees Celsius and will be able to provide a magnetic field up to 0.6 tesla [1]. This will ensure that all the heavy ion recoil charged particles, remaining in the beam, have the correct charged state. The Lorentz force is responsible for bending the moving particles and the first two dipole magnets are used to ensure the Lorentz force thoroughly filters the ions. The particles with the specified charge state will be bent an angle of 26 degrees while all other charged states will be bent more or less and not make it through the exit aperture [1].

St. George Hysteresis Measurements It was proposed to use a Hall probe to determine the magnetic field that influences the charged particles within the dipole magnet. To prevent the Hall probe from interfering with the ion beam, the Hall probe will be permanently mounted a fixed distance outside the region where the particles travel. The Hall probe will be placed approximately 5.5 inches from the center of the magnet. This position was chosen because a strong magnetic field still resides there while deflected particles will not collide with the probe there. To map out the change in the magnetic field with respect to the distance from the center of the dipole magnet and determine the magnetic field at the position the Hall probe will be mounted, a Hall probe was attached to a linear positioner. The magnetic field was then measured in 0.2 inch increments, up to ten inches, from the center of the magnet. These measurements were performed at five currents corresponding to five different magnetic fields. These currents started at a maximum of 120 amperes and decreasing by 20 percent of the maximum current down to 24 amperes. As shown in figure 1 the magnetic field is uniform near the center of the magnet and then drops off nonlinearly. The region of homogeneous magnetic field is the region where the ion beam will

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Figure 1. This shows the change in the magnetic field of dipole magnet B1 with respect to the distance from the center of the magnet.

The different line graphs represent different currents.

The magnetic field, inside the dipole magnet, does not vary perfectly linearly with the current through the magnet. This is due to the hysteresis of the dipole magnet. In order to stay on one hysteresis curve and make measurements on the dipole magnet, it was propose to vary the current in one direction only. This means the current must either start at zero amperes and always increase or the current must be increased to the maximum current and then always decreased. When varying the current, the magnetic field must first stabilize at the most extreme current before increasing or decreasing the current.

To determine if a Hall probe mounted 5.5 inches from the center of the dipole magnet is sufficient to determine the magnetic field charged particles experience in the center of the dipole magnet, an experiment was conducted with an NMR probe in the center of the magnet. For this

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experiment an NMR probe was held fixed at the center of the dipole magnet and a Hall probe was held fixed in its permanent position approximately 5.5 inches from the center of the magnet.

The current through the dipole magnet was then varied and the magnetic field readings on the Hall probe and the NMR probe were recorded. To show the hysteresis of the magnet, the current was varied by deceasing from the maximum of 130 amperes to the minimum of 0 amperes and by increasing from the minimum current to the maximum current. This procedure was done by varying the current in 2 ampere units. This experiment was conducted on the B1 and B2 dipole magnets of the St. George. Figures 2 and figure 3 show that on both magnets the field reading on the Hall probe varies linearly with the reading on the NMR probe. This means that a Hall probe mounted approximately 5.5 inches from the center of the magnet is sufficient to determine the magnetic field within the center of the magnet.

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Figure 2. Magnetic field reading on an NMR probe versus the magnetic field reading on a Hall probe and corresponding linear fits of the B1 magnet.

2 minute wait plot corresponds to waiting two minutes at zero current before increasing the current to the chosen magnetic field.

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Figure 3. Magnetic reading on an NMR probe versus magnetic field reading on a Hall probe and corresponding linear fit of the B2 magnet.

The current always decreased in developing this figure.





An additional experiment was conducted to determine the amount of time needed to allow the magnetic field within the dipole magnet to stabilize. This experiment was preformed to find the minimum amount of wait time needed to stabilize the dipole magnetic field. This was done by starting at either 0 or 130 amperes and waiting a specified time before increasing or decreasing to a desired magnetic field. This process was repeated several times waiting ten minutes, five minutes, and two minutes before changing the current. The process was repeated twenty five times for a two minute wait. Figure 2 shows the data from waiting two minutes falls on the hysteresis curve and has a linear fit close to the linear fit of the hysteresis curve. This means waiting at 0 or 130 amperes for two minutes is sufficient time to ensure accurate readings on the magnetic field probes.

Conclusion The Georgina project is ongoing due to equipment needs and further testing. With the code written for Georgina however, the project only needs minor equipment assembling to begin experiments. St. George is also an ongoing project. Equipment malfunctions have slowed down the development of the project. However, with experimental evidence validating the use of a permanently fixed Hall probe and the hysteresis data on two of the dipole magnets, experiments can be conducted much quicker once the project is completed. Once the Georgina and St.

George projects are fully operational the Nuclear Science Lab will be able to perform a wider

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range of tests and will have a combination of experimental techniques incomparable to that of any other lab in the world.

References [1] M. Couder et al. “Design of the recoil mass separator St. George.” Science Direct.

(2007):

35-45. Print [2] Garg, Umesh et al. “Development of GEORGINA.” (2009): Print [3] "Experimental Research, Institute for Structure and Nuclear Astrophysics (ISNAP), University of Notre Dame." University of Notre Dame. Web. 18 July 2011. http://www.nd.edu/~nsl/ html/research_exp.html.

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It is known that the interstellar medium is highly turbulent, but understanding the effects of that are still an active area of research. Possible sources of turbulence include supernovae explosions, solar winds, and the magneto-rotational instability, but as one of the main contributors, this simulation focuses on the effects of supernovae explosions. These are set up by injecting spheres of high energy near the midplane of the disk. This model sets up a stratified disk, as the interstellar medium varies in temperature with regions of cold gas (T 2000K), warm gas (2000K T 105K), and hot gas (T 105K). The stratified disk is kept in both hydrostatic and thermal equilibrium to prevent the disk from initially collapsing. The size of this disk is set to be 0.5 x 0.5 x 3.0 kpc3. A shearing sheet approximation is used to account for the galactic rotation and the periodic boundary conditions. This research aims to see how the magnetic fields in the interstellar medium are affected by turbulence. To this end, a small initial magnetic field is set up using ABC flows. Preliminary results indicate that the magnetic field is amplified after the supernovae explosions cause turbulence.

Introduction The Milky Way Galaxy has a radius of 20 kpc with a height of a couple hundred parsecs.

However, of that, only a small percentage of the mass of the entire galaxy is from the interstellar medium, or ISM, with most of the matter being confined to the disk (Lequeux 2005). Along with ordinary matter, the ISM contains cosmic rays and magnetic fields. These three components are bound together by electromagnetic forces with comparable pressures (Ferriere 2001).

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(2000 T 105K), and hot (T 105K). A stratified model takes this temperature distribution into account (Gent 2010).

Turbulence In a typical spiral galaxy the ISM is highly turbulent (Gressel 2008). This is caused by energy sources such as differential rotation, stellar radiation, high-energy particles, and energy given off from supernovae explosions (Lequeux 2005). Turbulence changes the balance of pressure and gravity to sub cloud scales as opposed to galactic scales, which then may regulate star formation (Joung MacLow 2006). These turbulent fields are established due to the presence of the driving mechanisms mentioned above as well as large length scales and low viscosities (Balsara 2005).

During a supernova explosion a shock wave, driven by the pressure of an expanding, hot gas bubble, is set up and moves into the surrounding area, sweeping up gas as it goes (Dyson 1997).

Gas in the ISM which has temperatures around a million Kelvin can be created by these explosions. However, this hot gas is confined in bubbles which are a result of clustered supernovae (Brandenburg 2007). Superbubbles can also be formed by stellar winds and supernovae explosions, and chimneys are formed when the expanding bubble runs into the stratified medium (de Avillez 2001).

Magnetic Field The study of magnetic fields in the ISM is a very active area of research. There are many questions that need to be answered, including what could be potential mechanisms for amplifying the field. Typically, in clouds the magnetic field has a strength of around 12μG while in the ISM it is closer to 3μG (Passot 1996). The magnetic field is somewhat organized on the galactic scale but, for the most part, the irregular components will dominate. The gravitational

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magnetic pressure at large scales (Lequeux 2005). The field on large scales is developed by a mean field dynamo but on smaller scales there are faster ways of generating fields (Balsara 2005). The correlation of small scale turbulence and a magnetic field leading to EMF can be described by the generation of a mean magnetic field explained by the α effect (Gressel 2008).

Heating and Cooling Another aspect that needs to be considered is the heating and cooling of the ISM. The cooling is done by emitting radiation. An atom, ion, or molecule gains energy from collisions and the energy is then radiated as a photon. The gas is heated by processes such as frictional heating, novae and supernovae, stellar winds, x-rays, cosmic rays, and starlight (Dyson 1997).

Description of the Model When setting up the stratified disk, the model needs to be in hydrostatic and radiative equilibrium. If not, the disk will collapse down to the midplane and be built back up until the pressure caused by turbulence is able to balance the process as done by Gressel (2008). To do

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where Γ is the heating function and Λ is the cooling function.

It can be seen in Figure 1 that temperature increases as the distance from the midplane increases,

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Figure 1: Illustrates the relationship between the normalized temperature, pressure, and density of the stratified model with a distance z from the midplane.

A small, initial magnetic field is set up using an ABC flow which sets the x,y,z components to be

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where v is the vector defined in equation 5, H is the scale height, and z is the distance from the midplane of the disk. The magnetic field can then be found using the fact that B = ∇ x A,which provides for a divergence free magnetic field (Balsara 2009).

To model the galactic rotation the values A = 14.82 ± 0.84 km s-1kpc-1, B = -12.37 ± 0.64 km skpc-1, and Ro = 8.5 ± 0.5 kpc are used and the shear parameter and rotation rate are found by using

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(Feast 2008).

Supernovae explosions are modeled by injecting spheres of high energy, on the order of 1051ergs, around the midplane of the disk, and the resulting shockwave provides the necessary turbulence.

Periodic boundary conditions are employed to map conditions at one boundary onto the corresponding boundary. This simulation models a section of the galactic disk which has dimensions of [-0.25, 0.25] x [-0.25, 0.25] x [-1.5 x 1.5] kpc and a resolution of 75x75x450 zones.

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Figure 2: This cross-section of the disk shows the density distribution at various time points after the supernovae explosions were set off.

With the preliminary results from the first run, graphs of the density were obtained. These graphs were taken from a cross-section of the disk over a time period of 20 Myr. At the beginning it can be seen that the density was very uniform. After some of the supernovae were set off it can be seen in the second image that there are some bubbles of lesser density, but on the whole the density is starting to increase around the midplane. The third image shows this

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by the fourth and final image.

Figure 3: a) This shows the rms velocity as a function of time and b) shows the rms magnetic field as a function of time.



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