1 RESEARCHING AND DESIGNING A SUITABLE ELECTROMAGNETIC SHIELD FOR T HE HYPERLOOP TRANSPORTATION POD Balvinder Kaur Dhillon Farah Ahmed Ali Dawoud Alexander Daniel Greenway 2 Abstract The hyperloop system is powered by an electromagnetic levitation system utilising systems such as linear induction motors, electrodynamic wheels, electromagnetic suspension and Halbach arrays. These subsystems produce electromagnetic radiation which could be harmful, especially to patients with implantable or portable medical devices. In this paper, research was conducted to further understand the potential effects of electromagnetic interference on the human body and on passengers implanted medical devices . Simulations were run on COMSOL to look at the shielding effects of five materials (Copper, Aluminium, Copper Alloy 770, Copper Beryllium, Pre - Tin Plated Stainless Steel and Silicon Carbide) to determine which material would be best suited for electromagn etic shielding of the hyperloop pod. The stimulation concluded that Copper - Beryllium was the best choice of material to be used for electromagnetic shielding. Biomedical Research Team Hyperlink, London, United Kingdom 07 th June 202 3 3 Table of Contents Abstract ________________________________ ________________________________ ____________________ 2 Introduction ________________________________ ________________________________ _________________ 4 Literature Review ________________________________ ________________________________ _____________ 5 1. Effects of Electromagnetic Radiation on individuals with and without medical devices and implants ______________ 5 A. Cardiovascular Device ________________________________ ________________________________ _____________________ 5 B. Orthopedic devices ________________________________ ________________________________ _______________________ 6 C. Neuromodulation Paragraph ________________________________ ________________________________ _______________ 7 D. Cochlear Implant Paragraph ________________________________ ________________________________ ________________ 8 E. Healthy Population ________________________________ ________________________________ _______________________ 9 2. EM Interference and Shielding ________________________________ ________________________________ _____ 10 3. Materials ________________________________ ________________________________ _______________________ 12 A. Copper ________________________________ ________________________________ ________________________________ 12 M ethodology ________________________________ ________________________________ _______________ 14 Linear Indu ction Motor ________________________________ ________________________________ ______________ 14 2. Linear Halbach Arrays ________________________________ ________________________________ _____________ 15 3. Simulation Design ________________________________ ________________________________ ________________ 16 Results ________________________________ ________________________________ ____________________ 17 Copper ________________________________ ________________________________ ___________________________ 17 Copper Beryllium ________________________________ ________________________________ ___________________ 17 3. Copper Alloy 770 ________________________________ ________________________________ _________________ 18 4. Aluminium ________________________________ ________________________________ ______________________ 19 5. Stainless Steel ________________________________ ________________________________ ___________________ 20 6. Silicon Carbide ________________________________ ________________________________ __________________ 21 Discussion ________________________________ ________________________________ __________________ 24 Conclusion ________________________________ ________________________________ _________________ 26 Bibliography ________________________________ ________________________________ ________________ 27 4 Introduction E lectromagnetic radiation plays an important role in modern day life and the human body is currently being constantly exposed to electromagnetic radiation while performing day to day activities. Most organisms are exposed to electromagnetic radiation daily , this can vary from devices with electronic components to those which use magnetism such as magnetic resonance imaging. Therefore, it is important to determine the effects of interference of the electromagnetic radiation emitted by devices to prevent any adverse side effects on humans and other organisms. Extensive research and studies have been conducted to further understand the negative effects of electromagnetic radiation on the human body to prevent any harmful health side effects that occur to the hu man body (Cirino, 2023). The hyperloop technology is designed to utilise several subsystems that will emit electromagnetic radiations. The electromagnetic radiation released by the hyperloop pod could have various effects on humans and therefore impact t he safety of the passenger. This paper aims to test the effect of the electromagnetic radiation on different passenger, ones with implanted medical devices and ones without, to ensure the design of the hyperloop pod is effective at avoiding any negative he alth side effects associated with the exposure to electromagnetic radiation. Since at the current time the pod is still in the research and development phase it will allow for new and innovative designs of the hyperloop pod to be created and developed to r educe any negative effects associated with the exposure of the passengers to electromagnetic radiation. The first phase of this paper was to perform a literature review into the effects of electromagnetic interference on healthy passengers and those wi th implanted medical devices. The primary devices of interest are cardiac assistance devices (such as pacemakers, left - ventricle assistance devices, and implanted defibrillators), deep - brain stimulation devices and techniques, orthopedic implants, and coch lear implants. The literature review then focused on conducting research to understand the mechanism of electromagnetic shielding and to understand what material properties are required. This was achieved by researching and further understanding the severa l concepts associated with electromagnetic shielding such as Schelkunoff’s law, faraday’s cage theory, and electromagnetic interference. After this research was conducted, five different materials were chosen as potential options due to their desirable ef ficient properties as electromagnetic shield. 5 In the second phase of this paper, the methodology section was completed to explain the theories and mechanisms used to design and test the shielding that will be used to prevent the effects of the elect romagnetic radiation. The experiment was designed by further understanding the linear induction motor and the linear Halbach array mechanisms that are involved in providing the propulsion for the hyperloop pod. The third phase was to design a small - scale d simulation of the Linear Halbach Array used in the propulsion system on COMSOL to simulate the effects of selected shielding materials for the pod to assist with developing a recommendation potential shielding materials. The selected materials were comme rcially pure Copper, Copper Alloy 700, Copper - Beryllium Alloy, Aluminum, Stainless Steel and Silicon Carbide. As for the final phase, the results obtained were reviewed and analysed in the discussion section to suggest improvement methods to ensure effectiveness in electromagnetic shielding for the hyperloop pod. Literature Review 1. Effects of Electromag netic Radiation on individuals with and without medical devices and implants A Cardiovascular Device Rese arch has shown that the effects of Electromagnetic fields on individuals with implantable cardiovascular devices, such as left ventricular assistance devices (LVAD), implantable cardiovascular defibrillators (ICD) and pacemakers are considered potentially dangerous. Patients with cardiovascular implants are at risk of localised heating of implants, movement of the implants, potential data acquisition problems, and potential misfires within the implants when patients are exposed to electromagnetic fields. Re search has shown that patients with implanted intracoronary stents could induce local heating and tissue damage when exposed to electromagnetic field with strengths of 7 Tesla. Research performed by Ishida et al (2020), recommended that people with implant able cardiovascular devices should be kept more than 6 inches away from any devices which may contain magnetic materials such as cell phones, headphones and radios, implying that electromagnetic interference could hold the potential to create signal noise and cause failure to activate the devices correctly. It is also noted that some systems that utilise larger fields such as anti - theft devices, metal detectors and some common household appliances such as microwave ovens can disturb and potentially cause th e device to 6 move from its usual position. Therefore, it could be concluded that the electromagnetic radiation could have a negative effect on passengers with cardiovascular device. B. Orthopedic devices Research was conducted to test the effects of e lectromagnetic radiation on orthopaedic devices. This was done by exposing individuals with knee and hip prosthesis to electromagnetic fields of 50 W/m2 and 100 W/m2 for six minutes (Crouzier et al., 2012). The results of the research showed that the elect romagnetic heating was <0.2 degrees Celsius and the induced tension created was 1.1V. This indicated that the results obtained did not lead to negative effects that could create potential health impacts on the patients, however it should be noted that at h igher electromagnetic field strengths could potentially increase the induced heating and tension to a significant amount. Chen et al. (2012), determined that in a spinal cord implant system (seen in figure 1) the induced heating during MRI exposure could c reate a temperature difference of up to 3.6 degrees Celsius (see table 1) between the biological matter and the implant which would likely cause noticeable discomfort for the patient. In conclusion, the current literature indicates that electromagnetic fie lds currently show no significant negative effects for patients with Orthopaedic devices when exposed to electromagnetic fields. Figure 1 : Positions for the fluorotic thermometry probes, #1 and #2, relative to the orthopedic implant, Basis Spinal System. Black arrows indicate the tip locations for temperature probes. 7 Table 1: Simulated and Measured Temperature Changes for 67 mm Length Implant in 1.5 - T/64 - MHz and 3 - T/128 - MHz MR Systems After 15 Minutes of RF Exposure at the Two Temperature Probe Locations for a Whole Body Averaged SAR of 2 W/k C. Neuromodulation Paragraph Deep brain stimulation (DBS) is a significant area of concern for electromagnetic interference as they are frequently affected by electromagnetic forces from the environment (see table 2). The two main outcomes of concern are on or off switching of the electrode array delivering unnecessary stimulation to the patient's central nervous system which could result in some minor effects such as low - level signal noise slightly altering the stimulation patterns and characteristics. T his could also potentially lead to irreversible brain or tissue damage. Blomstedt et al, performed a trial on 172 patients with implantable DBS systems (2006) through a patient survey to analyse the effects of electromagnetic fields experienced due to the implant. They identified that 20 patients had the pulse generator within their DBS systems which turned off when the patients were to electromagnetic sources. In two patients, the Itrel II IPG DBS systems had to be replaced with electromagnetically shielde d Kinetra IPG DBS systems (both produced by Medtronic Inc., Minneapolis, MN, USA) because the electromagnetic radiation severely damaged the DBS systems, 6 of the 172 patients in the study had pacemakers and in two patients these pacemakers led to interfer ence between the systems. The conclusion of their research was that strong external electromagnetic interference could be considered a severe threat to patient safety and malfunction of DBS systems and in a few reported cases, has resulted in severe neurol ogical damage. 8 Table 2: Patients with Unintended Deactivation of the IPG (Blomstedt et al, 2006) Patient Target IPG Suspected Source of Interference 1 STN Itrel II Theft detector 2 VIM Soletra Theft detect electric weld or, 3 STN Kinetra Theft detector 4 STN Itrel II Security airport gate at 5 STN Itrel II Security airport gate at 6 VIM Itrel II Security airport gate at 7 STN Itrel II Security airport, lou gate dspeaker at 8 STN Itrel II loudspeaker 9 STN Itrel II loudspeaker 10 VIM Itrel II loudspeaker 11 STN Itrel II Voice memory 12 STN Itrel II Mobile phone 13 STN Itrel II Dentist visit 14 VIM Itrel II Dentist visit 15 VIM Itrel II Electrocardiogram 16 STN Itrel II Lightning rod 17 GPI Itrel II Electric weld, electric drill bur 18 STN Itrel II Security cortege 19 STN Kinetra Electric network/high voltage line 20 GPI Kinetra Electric network/high voltage line D. Cochlear Implant Paragraph Research was conducted where patients with cochlear implants were exposed to electromagnetic field strengths of 0.2 and 1.5 Tesla, during Magnetic Resonance Imaging (MRI), no negative effects were observed on the patients (Teissl et al., 1998). Therefore, it could be concluded that the electromagne tic forces generated by the hyperloop tube will cause no significant effect on patients with cochlear implants. 9 E. Healthy Population The focus of this literature review has been on individuals who use medical devices and how electromagnetic fields may affect those individuals. However, the effects that electromagnetic radiation has on healthy individuals should also be noted because electromagnetic fields can affect several of the bodies vital systems and it is essential to examine how different pas sengers are affected. One such system is the cardiovascular system, Griefahn et al., (2002) determined that frequencies between 0Hz and 300Hz can cause elevated heart rates in humans. Furthermore, frequencies between 300Hz and 100kHz can cause an increase in mean ECG potential (Fang et al., 2016), and frequencies between 100kHz and 300GHz can cause a decreased heart rate while lying down (Misek et al., 2018). In addition to the cardiovascular effects, magnetic fields have been determined to induce electrica l currents within the peripheral nervous system which can, in severe cases, prevent breathing and cause ventricular fibrillation. Exposure to electromagnetic fields also has the potential to increase the risk of dementia, motor neurone disease, multiple sc lerosis, and epilepsy (Funk and Fähnle, 2021). Nausea, vertigo, and dizziness have all been reported by patients and staff near MRI scanners for significant periods of time due to the electromagnetic fields produced (Chakeres and de Vocht, 2005). Cavin et al. (2017) determined that sour and bitter taste like a metallic one was experienced by 50% of subjects when exposed to 2T of electromagnetic radiation. Electromagnetic fields also affect the brain’s cognitive ability in addition to the neurological effect s. Studies have found that at 8T, subjects had a short - term memory loss and at 1.5T there were 4% reductions in eye - coordination tests and 16% reductions in visual contrast sensitivity (Chakeres and de Vocht, 2005), a different study found that children wo rking memory was negatively affected when exposed to low frequency EMF. Saliev et al., (2019) demonstrated that EMF has negative implications on the reproductive system, decreasing sperm motility and viability, additionally Odaci et al., (2015) determined that pregnant rats exposed to a 900 MHz frequency of EMF showed a higher apoptotic index with increased DNA oxidation. Musculoskeletal effects have also been researched, Stoltny et al., (2015) determining that 3T - 5T of exposure has no direct effect of the micrometrical parameters of the long and short bones, there was, however, a modification of the bone mineralisation process, directly impacting the mechanical properties of the bone. Additionally, the researchers determined that the isometric contractions decreased by 8% compared to that of an original skeletal muscle, demonstrating a severe weakening of the contractions. Respiratory effects have been discovered as well, T - cells have been shown to drop by 20 - 30 percent (Albalawi, A., Mustafa, M. and Masood. , 2022). It can be reasonably inferred that this is likely to cause symptoms including constant headaches and shortness of breath for patients exposed to this environment. Additionally, after a 20 - hour exposure period, the leakrelated respiration increased , a metric which is associated with altered mitochondrial activity and a shortness of breath, which is likely the cause of the patients’ oxygen consumption increasing, (Lasalvia et al, 2022). For these various reasons, it can be inferred that with effectiv e shielding that the majority of the healthy population will not feel any side - effects, however without shielding passengers could be subjected to significant discomfort caused by the propulsion system. 10 2. EM Interference and Shielding Electromagnetic shielding is the protection of electromagnetically sensitive components or objects from external electromagnetic field. This is performed by absorbing or re - distributing the electromagnetic waves that the components interact with. Therefore, when selectin g the material that will be used as an electromagnetic shielding it is important for non - ionizing radiation properties to be present and the material must have high conductivity, a high dielectric constant, or a high magnetic permeability. These propertie s are necessary so that when the waves encounter the shielding material it is repeatedly reflected, absorbed, and refracted so that the amount of electromagnetic interference that passes through is minimal. The selected materials significantly contribute t o the effectiveness of the shielding, therefore in this paper several materials with the required properties will be tested to ensure the best electromagnetic shielding material is used for the hyperloop pod shielding. Electromagnetic shielding is usuall y measured through the efficacy of its shielding abilities. This is a measurement of the attenuation of the electromagnetic signal through a shielding material, as it is lost through reflection, absorption, and refraction according to Schelkunoff’s electro magnetic shielding theory (1943). In this theory the shielding effect of a metal is expressed as: 𝑆𝐸 = 𝑅 + 𝐴 + 𝐵 (Eq. 1) Where SE is the shielding effectiveness (in dB), B is the corrosion factor due to multiple reflections within the material, R is the reflection loss (in dB), and A is the absorption loss (in dB). When neglecting the correction factor B (due to multiple ref lections), the shielding effectiveness equation can be rewritten as: 𝑆𝐸 = 𝑅 + 𝐴 (Eq. 2) For a plane electromagnetic field, the absorption and reflection losses can be determined using the below equations: 𝐴 = 0.131 𝑡 ( 𝑓𝜇 ! 𝜎 ! ) # (Eq. 3) 11 Where, A is the electrical conductivity relative to copper, f is the frequency of the signal, t is the thickness of the material in mm, and 𝜇 ! is the permeability relative to free space and 𝜎 ! is the electrical conductivity relative to copper (Kumar Mishra, 2019). Electromagnetic shielding is related to Schelkunoff’s theory as shielding action is portrayed similarly to the passage of electromagnetic signals through a transmission line. The experiment suggested that when energy passes through a transmission line it faces a disparity between the resistances of the terminating load and transmission line. It will be reflected and absorbed at different amounts solely depending on the ratio of the resistances. Schelkunoff’s theory suggests that the shielding effect occurs due to reflection losses that occur at shield boundaries combined with the absorption occurring in the shield itself. Shield thickness is required to be at least 1 skin depth (skin depth ( 𝛿 $ ) is the distance required to decrease the magnetic field streng th by a factor of 1/e) as shield thickness plays a fundamental role in governing the shielding effect. The transmission line and multiple reflection models were used to develop the Effectiveness Equations which conclude that in a high - loss case, the overal l shielding is the sum of the output reflection losses and single - pass input, and the single - pass transmission line attenuation. As for the low - loss case the shielding equations form a lumped model with the shield being replaced by its direct current imped ance (Kumar Mishra, 2019). Schelkunoff’s theory states that the theory can be used to accurately represent the physical effects occurring with the transmission line that carries electromagnetic waves between points (Kunkel, 2014). The theory also states t hat the reflective coefficients provided by the wave theory are like those identified by radiated waves striking a shielding barrier (J. Mohr, 2008). In the theory multiple reflection solutions and transmission line models were used to determine the electr omagnetic shield equations. Observations then showed that the total electromagnetic shielding effect could be obtained through the sum of the single - pass transmission line attenuation, single - pass input, and output reflection losses (J. Mohr, 2008). This theory is related to the Faraday Cage, which was used to determine the properties of magnetic shielding and preventing multiple electromagnetic waves from interfering. The Faraday Cage demonstrated the theory of electromagnetic induction, which in turn, re inforces the idea of electrostatic induction dealing with electrical fields. Theoretically, these cages can block 100% of electromagnetic field radiation with the correct conductive material. One example of a Faraday Cage being employed is as shielding wit hin the walls of a hospital room containing an MRI machine, as these machines create very strong fields these fields must be contained within the room so that they do not interact or disrupt the equipment elsewhere in the building (Executive, 2022). 12 3 Materials A. Copper Copper has high thermal and electrical conductivity, allowing it to be able to absorb magnetic and electric waves effectively which reduces their negative effects on the passengers inside the hyperloop pod. In addition to this, t he mechanical properties of copper allow the material to be easily shaped and bent into the required shape of the pod. The lifespan of the product would also be long due to the high corrosion resistance properties. Copper has 29 electrons, with 14 spinni ng in one direction and 15 in the other causing Copper to be a stable element. When Copper is approached by a magnetic field the surface electrons begin to rotate opposite to the magnetic field creating resistance to the applied field, and in turn creating their own magnetic field. The combination of thermal and electrical conductivity and the atomic structure are the reason that Copper is widely considered the best shielding material and is regarded as the international standard for electrical properties. B. Copper Alloy 770 Copper Alloy 770 is comprised 55% Copper, 18% Nickel, and 27% Zinc. This material is used in EM shielding due to the corrosion resistant properties. Alloy 770 is efficient at EMI shielding when the frequency is in the 500KHz to GHz range. This material is commonly used because it has a relative permeability of 1 making it ideal in applications such as MRI. Therefore, Copper Alloy 770 is a good material for shielding, as while it does offer good magnetic shielding properties, the resistance to corrosion make s it an improved choice over commercial purity copper. C. Copper Beryllium Alloy This material is a common material used for EMI shielding of the radio frequency range and has many applications, specifically in military electronics, and telecommunicati ons. This material has excellent conductivity and can distribute currents through three dimensions. In addition, it is an excellent material for use because of its high strength and fatigue resistance properties which can allow it to undergo repeated movem ent and will allow it to withstand cyclic stresses, in turn preventing fatigue failure. The material also has ideal processing properties and corrosion resistance properties making it an ideal material choice. 13 D. Aluminum Aluminium is considered a go od magnetic shield at high frequencies such as 30 to 100 MHz range. Aluminium provides a minimum of 85dB of shield effectiveness when exposed to electromagnetic frequencies range of 30 to 100MHz. Since no research showed that aluminium is a good electromag netic shield at low frequencies there are concerns that at low frequencies the shielding effects are not adequate for use in the hyperloop pod. The permeability of pure aluminium when compared to air makes it an inadequate material to use for magnetic shie ld as a thick layer is required to achieve the minimum effectiveness. There is also concern with the rate of degradation as research shows that the degradation increases with increased magnetic field exposure due to the metallic microstructure and weak met allic bonding. Therefore, the quality of the shielding properties must be offset by increasing the amount of material present in the shield, potentially negating any benefit from the lower density. E. Stainless Steel Stainless Steel (SS) is an increasingly popular choice of shielding material, primarily for use within protective clothing. It has been shown that SS is a very effective shielding material when conductive SS fibres are added to polymers for use in textiles and it could be used as re gular shielding material. For example, Stainless Steel, Ferritic, S44627, annealed, has an average of 2.8 %IACS indicating acceptable electrical conductivity for the dissipation and absorption of electromagnetic fields, making it a suitable material for el ectromagnetic shielding F. Silicon Carbide Recently, light weight and high - performance shielding materials have seen significantly more research activity and funding than previously. Research has shown that Silicon Carbide is an effective electromagnetic shield. Silicon Carbide (SiC) is a type of ceramic matrix composite (a class of materials which is characterised by low density), high strength, good oxidation resistance, and excellent thermo - physical stability which would allow it to work excellently as a high temperature electromagnetic field shielding material. The lightweight semiconductor behaviour and high dielectric loss also make SiC an interesting choice of material. However, as the electrical conductivity is low SiC isn’t sufficiently able to meet the high requirements for commercial use. If this material is considered f urther, it must be improved by adding conductive materials such as pyrolytic carbon interphase (PyC) of carbon fiber (Cf) (Ding et al, 2013). It has been discovered that SiC with 3.3 vol% PyC displays shielding effectiveness around 25dB (Mu et al, 2015), a nd SiC with 40 vol% Cf achieves approximately 43dB of shielding effectiveness (Chen et al, 2015). This shows that Silicon Carbide should be considered for the shielding material, however this material couldn’t be simulated in COMSOL due to a lack of availa ble material properties so standard Silicon Carbide has been simulated. 14 M ethodology T here are numerous mechanisms used as part of the propulsion system and levitation. The mechanism that is the primary focus of the simulations is the linear induction motor and the linear Halbach array which provide the propulsion for the pod. 1. Linear Indu ction Motor Linear induction motors work similarly to regular induction motors. There are two sections, the primary section generates magnetic fields across an airgap, which in turn induces forces to the secondary section which a cts as a conductor. The primary section, which is built into the pod, generates the varying magnetic fields and this requires a power source for this section to have a power - source built into the pod adding a significant source of weight. The energy losses proportional to the pod length is larger when the pod is shorter due to the power source weig ht to pod length ratio being smaller , however, due to the pods being small the design and construction of the guideway will be cheap as no active component will be required , except for the secondary component. Figure 2 : An example of a linear induction motor (Zhang et al, 20 20) 15 2. Linear Halbach Arrays Halbach arrays are orientations of permanent magnets with two distinctive fields on either side of the array. On one side there is a strong magnetic field whereas on the other side there is a weak magnetic field making it an ideal process for harvesting en ergy as the magnetic array travels over the conductive surface. This is because as the pod travels over the conductive surface eddy currents are induced within the within the surface, each of which creates a counter magnetic field opposing the change in ma gnetic field that it has created, according to Lenz’s Law. The result of this phenomenon is that electromagnetic drag forces on the sheet are created opposing the movement of the magnetic array over it. Inducing eddy currents in the surface also in turn ca uses upwards Lorentz forces on the magnets lifting them up. The Lorentz force is the force responsible for the magnetic levitation, meaning that the magnetic drag must be smaller than the Lorentz force so that the pod is able to accelerate. Once a large en ough Lorentz force has been achieved the pod will then be able to levitate (Kooger, 2016). Figure 3: Halbach arrays. (Wang et al, 2018) 16 3. Simulation Design Figure 4: The COMSOL Simulation of the Linear Halbach Array without Air Figure 5: The COMSOL Simulation of the Linear Halbach Array with Air The simulations above show the Linear Halbach Array that was designed and simulated in COMSOL. In Figure 4 the simul ation is shown without air boundaries so that it is easier to see the different components. The top panel is the material that is being simulated as shielding. The next rectangle below that is the stator back yoke, is attached to the stator teeth (the larg e downwards rectangles), each of which has a coil on either side with 120 turns on each coil. The rectangles below the stator teeth are magnets which are arranged so that they alternate between producing upwards and downwards magnetic fields and they in tu rn are attached to the magnets back yoke. In Figure 5 we see the same simulation when it is enclosed in air to simulate a vacuum as the magnetic and electrical properties of air are negligible and effectively simulate a vacuum. Once the Linear Halbach Arr ay had been created, two studies were performed upon it. The first was a stationary study to determine the current angle sweep, and the second of which was a transient study. The magnetic flux densities of the stationary and transient studies were then ext racted and compared for each material against copper, as can be seen below. The current angle sweep (stationary study) calculated the electromagnetic flux density throughout the array at the optimum current angle which creates the largest electromagnetic f lux densities, while the transient study takes this optimum current angle and applies motion to the magnet to account for any movement, which then calculates those electromagnetic field densit 17 Results 1. Copper Figure 6 : The Stationary S tudy of Copper Shielding Figure 7 : The Transient Stud y of Copper shielding Figures 6 and 7 show us the magnetic flux densities in the Commercially pure Copper shielding 2. Copper Beryllium Figure 8 : The Stationary Study of Copper Beryllium Shielding Figure 9 : A comparison of the Stationary Study Result s for Copper Beryllium and Copper Shielding Figure 10 : The Transient Study of Copper Beryllium Shielding 18 Figure 11: A comparison of the Transient Study Results for Copper Beryllium and Copper Shielding While we can see that figure 8 appears identical to figure 6, we can see that figure 9 shows that there is a slightly larger magnetic flux density throughout the entire Halbach array during the stationary study, whereas figure 11 shows that during the transient study the magnetic flux density is generally smaller than the magnetic flux density of the commercially pure Copper shielding. 3. Copper Alloy 770 Figure 12: T he Stationary Study of Copper Alloy 770 Shielding Figure 13: A comparison of the Stationary Study Results for Copper Alloy 770 and Copper Shielding Figure 14: The Transient Study of Copper Alloy 770 Shielding Figure 15: A comparison of the Transient Study Results for Copper Alloy 770 and Copper Shielding. While figures 13 and (especially) 15 appear to signify a very large difference in the magnetic flux den sity, it should be mentioned that the magnitude of any differences present is at the scales of 10 " #$ and 10 " # % respectively, showing that on a scaled - down model the differences are negligible. 19 4. Aluminium Figure 16: The Stationary Study of Aluminium Shielding Figure 17: A comparison of the Stationary Study Results for Aluminium and Copper Shielding Figure 18: The Transient Study of Aluminium Shielding Figure 19: A comparison of the Transient Study Resu lts for Aluminium and Copper Shielding Figures 17 and 19 appear to show a significant difference in the in the magnetic flux densities the scale of the difference renders any differences negligible. 20 5. St ainless Steel Figure 20: The Stationary Study of Stainless - Steel Shielding Figure 21: A c omparison of the Stationary Study Results for Stainless Steel and Copper Shielding Figure 22: The Transient Study of Stainless - Steel Shielding Figure 23: A comparison of the Transient Study Results for Stainless - Steel and Copper Shielding Figures 21 and 23 appear to show a significant difference in the in the magnetic flux densities the scale of the difference renders any differences negligible.