• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.42.2-43
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• 2018

When galaxy clusters interact, the intergalactic gas collides, forming shocks that are characterized by a low sonic Mach number (~3) but a comparatively high Alfvenic Mach number (~30). Such shocks behave differently from the more common astrophysical shocks, which tend to have higher sonic Mach numbers. We wish to determine whether these shocks, despite their low sonic Mach number, are capable of accelerating particles and thereby contributing to the cosmic ray spectrum. Using the PIC-MHD method, which separates the gas into a thermal and a non-thermal component to increase computational efficiency, and relying on existing PIC simulations to determine the rate at which non-thermal particles are injected in the shock, we investigate the evolution of galaxy cluster shocks and their ability to accelerate particles. Depending on the chosen injection fraction of non-thermal particles into the shock, we find that even low-Mach shocks are capable of accelerating particles. However, the interaction between supra-thermal particles and the local magnetic field triggers instabilities and turbulence in the magnetic field. This causes the shock to weaken, which in turn reduces the effectiveness of the supra-thermal particle injection. We investigate how this influences the shock evolution by reducing the particle injection rate and energy and find that a reduction of the particle injection fraction at this stage causes an immediate reduction of both upstream and downstream instabilities. This inhibits particle acceleration. Over time, as the instabilities fade, the shock surface straightens, allowing the shock to recover. Eventually, we would expect this to increase the efficiency of the particle injection and acceleration to previous levels, starting the same series of events in an ongoing cycle of increasing and decreasing particle acceleration.

• Journal of The Korean Astronomical Society
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• v.36 no.3
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• pp.111-121
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• 2003

In order to explore the cosmic ray acceleration at the cosmological shocks, we have performed numerical simulations of one-dimensional, plane-parallel, cosmic ray (CR) modified shocks with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. Based on the hypothesis that strong Alfven waves are self-generated by streaming CRs, the Bohm diffusion model for CRs is adopted. The code includes a plasma-physics-based 'injection' model that transfers a small proportion of the thermal proton flux through the shock into low energy CRs for acceleration there. We found that, for strong accretion shocks with Mach numbers greater than 10, CRs can absorb most of shock kinetic energy and the accretion shock speed is reduced up to $20\%$, compared to pure gas dynamic shocks. Although the amount of kinetic energy passed through accretion shocks is small, since they propagate into the low density intergalactic medium, they might possibly provide acceleration sites for ultra-high energy cosmic rays of $E\ll10^{18}eV$. For internal/merger shocks with Mach numbers less than 3, however, the energy transfer to CRs is only about $10-20\%$ and so nonlinear feedback due to the CR pressure is insignificant. Considering that intracluster medium (ICM) can be shocked repeatedly, however, the CRs generated by these weak shocks could be sufficient to explain the observed non-thermal signatures from clusters of galaxies.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.49.1-49.1
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• 2019

Giant radio relics in the outskirts of galaxy clusters have been observed and they are interpreted as synchrotron emission from relativistic electrons accelerated via diffusive shock acceleration (DSA) in weak shocks of Ms < 3.0. In the DSA theory, the particle momentum should be greater than a few times the momentum of thermal protons to cross the shock transition and participate in the Fermi acceleration process. In the equilibrium, the momentum of thermal electrons is much smaller than the momentum of thermal protons, so electrons need to be pre-accelerated before they can go through DSA. To investigate such electron injection process, we study the electron pre-acceleration in weak quasi-perpendicular shocks (Ms = 2.0 - 3.0) in an ICM plasma (kT = 8.6 keV, beta = 100) through 2D particle-in-cell simulations. It is known that in quasi-perpendicular shocks, a substantial fraction of electrons could be reflected upstream, gain energy via shock drift acceleration (SDA), and generate oblique waves via the electron firehose instability (EFI), leading the energization of electrons through wave-particle interactions. We find that such kinetic processes are effective only in supercritical shocks above a critical Mach number, $Ms{\ast}{\sim}2.3$. In addition, even in shocks with Ms > 2.3, energized electrons may not reach high energies to be injected to DSA, because the oblique EFI alone fails to generate long-wavelength waves. Our results should have implications for the origin and nature of radio relics.

• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.405-412
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• 2004

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc $\ge$ 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to ${\~}50\%$ in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks ($M_s {\le} 5$), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.101.2-101.2
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• 2012

Shocks are ubiquitous in astrophysical plasmas: bow shocks are formed by the interaction of solar wind with planetary magnetic fields, and supernova explosions and jets produce shocks in interstellar and intergalactic spaces. The global morphologies of these shocks are usually described by a set of magnetohydrodynamic (MHD) equations which tacitly assumes local thermal equilibrium, and the resulting Rankine-Hugoniot shock jump conditions are applied to obtain the relationship between the upstream and downstream physical quantities. While thermal equilibrium can be achieved easily in collisional fluids, it is generally believed that collisions are infrequent in astrophysical settings. In fact, shock widths are much smaller than collisional mean free paths and a variety of kinetic phenomena are seen at the shock fronts according to in situ observations of planetary shocks. Hence, both the MHD and kinetic equations have been adopted in theoretical and numerical studies to describe different aspects of the physical phenomena associated with astrophysical shocks. In this paper, we present the results of 3D relativistic particle-in-cell (PIC) simulations for ion-electron plasmas, with focus on the shock structures: when a jet propagates into an unmagnetized ambient plasma, a shock forms in the nonlinear stage of the Weibel instability. As the shock shows the structures that resemble those predicted in MHD systems, we compare the results with those predicted in the MHD shocks. We also discuss the thermalization processes of the upstream flows based on the time evolutions of the phase space and the velocity distribution, as well as the wave spectra analyses.

• Nuclear Engineering and Technology
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• v.52 no.11
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• pp.2638-2651
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• 2020

Nozzle corner cracks present at the intersection of reactor pressure vessels (RPVs) and inlet or outlet nozzles have been a persistent problem for a number of years. The fracture analysis of such nozzle corner cracks is very important and critical for the efficient design and assessment of the structural integrity of RPVs. This paper aims to perform an engineering critical assessment of RPVs with nozzle corner cracks subjected to several transients accompanied by pressurized thermal shocks. The critical crack size of the RPV model with nozzle corner cracks under transient loading is evaluated on failure assessment curve. In particular, the influence of cladding on the crack initiation of nozzle corner crack under thermal transients is studied. The influence of primary internal pressure and secondary thermal stress on the stress field at nozzle corner and SIF at crack front is analyzed. Finally, the influence of different crack size and crack shape on the final critical crack size is analyzed.

• Journal of The Korean Astronomical Society
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• v.35 no.4
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• pp.159-174
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• 2002

Cosmological hydrodynamic simulations of large scale structure in the universe have shown that accretion shocks and merger shocks form due to flow motions associated with the gravitational collapse of nonlinear structures. Estimated speed and curvature radius of these shocks could be as large as a few 1000 km/s and several Mpc, respectively. According to the diffusive shock acceleration theory, populations of cosmic-ray particles can be injected and accelerated to very high energy by astrophysical shocks in tenuous plasmas. In order to explore the cosmic ray acceleration at the cosmic shocks, we have performed nonlinear numerical simulations of cosmic ray (CR) modified shocks with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. We adopted the Bohm diffusion model for CRs, based on the hypothesis that strong Alfven waves are self-generated by streaming CRs. The shock formation simulation includes a plasma-physics-based 'injection' model that transfers a small proportion of the thermal proton flux through the shock into low energy CRs for acceleration there. We found that, for strong accretion shocks, CRs can absorb most of shock kinetic energy and the accretion shock speed is reduced up to $20\%$, compared to pure gas dynamic shocks. For merger shocks with small Mach numbers, however, the energy transfer to CRs is only about $10-20\%$ with an associated CR particle fraction of $10^{-3}$. Nonlinear feedback due to the CR pressure is insignificant in the latter shocks. Although detailed results depend on models for the particle diffusion and injection, these calculations show that cosmic shocks in large scale structure could provide acceleration sites of extragalactic cosmic rays of the highest energy.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.1
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• pp.56.2-56.2
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• 2018

Astrophysical shocks accelerate particles to high velocities, which we observe as cosmic rays. The acceleration process changes the nature of the shock because the particles interact with the local magnetic field, removing energy and potentially triggering instabilities. In order to simulate this process, we need a computational method that can handle large scale structures while, at the same time, following the motion of individual particles. We achieve this by combining the grid magnetohydrodynamics (MHD) method with the particle-in-cell (PIC) approach. MHD can be used to simulate the thermal gas that forms the majority of the gas near the shock, while the PIC method allows us to model the interactions between the magnetic field and those particles that deviate from thermal equilibrium. Using this code, we simulate shocks at various sonic and Alfvenic Mach numbers in order to determine how the behaviour of the shock and the particles depends on local conditions.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.1
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• pp.45.1-45.1
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• 2011

Shock waves form in the intergalactic medium as a consequence of accretion, merger, and turbulent motion during the structure formation of the universe. They not only heat gas but also govern non-thermal processes through the acceleration of cosmic rays (CRs), production of magnetic fields, and generation of vorticity. We examine diffusive shock acceleration of the pre-existing as well as freshly injected populations of nonthermal, CR particles at weak cosmological shocks. Since the injection is extremely inefficient at weak shocks, the pre-existing CR population dominates over the injected population. If the pressure due to pre-existing CR protons is about 5 % of the gas thermal pressure in the upstream flow, the downstream CR pressure can absorb typically a few to 10 % of the shock ram pressure at shocks with the Mach number M<3. Yet, the re-acceleration of CR electrons can result in a substantial synchrotron emission behind the shock. The implication of our findings for observed bright radio relics is discussed.

• Journal of Ocean Engineering and Technology
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• v.12 no.1
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• pp.58-64
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• 1998

An analysis method for the reliability of ceramic structures subjected to thermal shocks is presented. Flaws with the size of given probability distribution function are assumed to be distributed at random with a certain density per unit volume in the structures. Criterions for crack instability are derived for brittle solids under general thermal stresses. A probabilistic failure model is presented to study the probability of crack instability for brittle solids containing cracks with uncertain size. The reliabilities of brittle structures are evaluated based on the weakest-link hypothesis, which states that a structure fails when the cracks in any differential volume become unstable. A numerical example is given to demonstrate the application of the proposed method.