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K C Shaing - One of the best experts on this subject based on the ideXlab platform.
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neoclassical toroidal Plasma Viscosity with effects of finite banana width for finite aspect ratio tokamaks
Physics of Plasmas, 2016Co-Authors: K C Shaing, S. A. SabbaghAbstract:Theory for neoclassical toroidal Plasma Viscosity has been developed to model transport phenomena, especially, toroidal Plasma rotation for tokamaks with broken symmetry. Theoretical predictions are in agreement with the results of the numerical codes in the large aspect ratio limit. The theory has since been extended to include effects of finite aspect ratio and finite Plasma β. Here, β is the ratio of the Plasma thermal pressure to the magnetic field pressure. However, there are cases where the radial wavelength of the self-consistent perturbed magnetic field strength B on the perturbed magnetic surface is comparable to the width of the trapped particles, i.e., bananas. To accommodate those cases, the theory for neoclassical toroidal Plasma Viscosity is further extended here to include the effects of the finite banana width. The extended theory is developed using the orbit averaged drift kinetic equation in the low collisionality regimes. The results of the theory can now be used to model Plasma transpo...
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neoclassical Plasma Viscosity and transport processes in non axisymmetric tori
Nuclear Fusion, 2015Co-Authors: K C Shaing, K Ida, S. A. SabbaghAbstract:Neoclassical transport processes are important to the understanding of Plasma confinement physics in doubly periodic magnetized toroidal Plasmas, especially, after the impact of the momentum confinement on the particle and energy confinement is recognized. Real doubly periodic tori in general are non-axisymmetric, with symmetric tori as a special case. An eight-moment approach to transport theory with Plasma density N, Plasma pressure p, mass flow velocity V and heat flow q as independent variables is adopted. Transport processes are dictated by the solutions of the momentum and heat flux balance equations. For toroidal Plasma confinement devices, the first order (in the gyro-radius ordering) Plasma flows are on the magnetic surface to guarantee good Plasma confinement and are thus two-dimensional. Two linearly independent components of the momentum equation are required to determine the flows completely. Once this two-dimensional flow is relaxed, i.e. the momentum equation reaches a steady state, Plasmas become ambipolar, and all the transport fluxes are determined through the flux–force relation. The flux–force relation is derived both from the kinetic definitions for the transport fluxes and from the manipulation of the momentum and heat flux balance equations to illustrate the nature of the transport fluxes by examining their corresponding driven forces and their roles in the momentum and heat flux balance equations. Steady-state Plasma flows are determined by the components of the stress and heat stress tensors in the momentum and heat flux balance equations. This approach emphasizes the pivotal role of the momentum equation in the transport processes and is particularly useful in modelling Plasma flows in experiments. The methodology for neoclassical transport theory is applied to fluctuation-driven transport fluxes in the quasilinear theory to unify these two theories. Experimental observations in tokamaks and stellarators for the physics discussed are presented.
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neoclassical toroidal Plasma Viscosity in the vicinity of the magnetic axis in tokamaks with broken symmetry
Physics of Plasmas, 2015Co-Authors: K C Shaing, H H Lee, J Seol, A Y AydemirAbstract:Theory for neoclassical toroidal Plasma Viscosity in the low collisionality regime is extended to the vicinity of the magnetic axis in tokamaks with broken symmetry. The toroidal Viscosity is induced by particles drifting off the perturbed magnetic surface under the influence of the symmetry breaking magnetic field. In the region away from the magnetic axis, the drift orbit dynamics is governed by the bounce averaged drift kinetic equation in the low collisionality regimes. In the vicinity of the magnetic axis, it is the drift kinetic equation, averaged over the trapped particle orbits, i.e., potato orbits, that governs the drift dynamics. The orbit averaged drift kinetic equation is derived when collision frequency is low enough for trapped particles to complete their potato trajectories. The resultant equation is solved in the 1/ν regime to obtain transport fluxes and, thus, toroidal Plasma Viscosity through flux-force relation. Here, ν is the collision frequency. The Viscosity does not vanish on the ma...
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numerical validation of the refined formula of neoclassical toroidal Plasma Viscosity in tokamaks
Nuclear Fusion, 2013Co-Authors: Youwen Sun, K C Shaing, Y Liang, Baogen Shen, B N WanAbstract:Neoclassical toroidal Plasma Viscosity (NTV) theory in collisionless regimes in tokamaks has been well developed in the past. The NTV evaluated from the connected formula developed by Shaing et al (2010 Nucl. Fusion 50 025020) was in good agreement with the numerical results in most cases. The boundary condition in the superbanana plateau regime has been found to be important in the numerical modelling when the resonant pitch is close to the boundaries of the pitch angle space, but it was not included in the original connected formula. This generates a big discrepancy between the numerical results and those evaluated from the smoothly connected formula as the resonant pitch is close to 0 or 1. Recently, the connected formula was refined. In this paper, we present the method of how to apply this refinement for practical NTV modelling and demonstrate the improvement of this refined formula by comparing the results evaluated from it with the numerical ones. Some techniques are developed to accurately model the NTV with the refined formula. The accuracy of the results modelled from the refined formula is strongly improved over the previous formula as the resonant pitch is close to 0 or 1 and they agree very well with the numerical ones.
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theory for neoclassical toroidal Plasma Viscosity in tokamaks
Plasma Physics and Controlled Fusion, 2012Co-Authors: S. A. Sabbagh, C T Hsu, M S Chu, K C Shaing, Jae Chun Seol, Y SunAbstract:Error fields and magnetohydrodynamic modes break toroidal symmetry in tokamaks. The broken symmetry enhances the toroidal Plasma Viscosity, which results in a steady-state toroidal Plasma flow. A theory for neoclassical toroidal Plasma Viscosity in the low-collisionality regimes is developed. It extends stellarator transport theory to include multiple modes and to allow for |m???nq|???1. Here, m is the poloidal mode number, n is the toroidal mode number and q is the safety factor. The bounce averaged drift kinetic equation is solved in several asymptotic limits to obtain transport fluxes. These fluxes depend non-linearly on the radial electric field except for those in the 1/? regime. Here, ? is the collision frequency. The theory is refined to include the effects of the superbanana plateau resonance at the phase space boundary and the finite ?B drift on the collisional boundary layer fluxes. Analytical expressions that connect all asymptotic limits are constructed and are in good agreement with the numerical results. The flux?force relations that relate transport fluxes to forces are used to illustrate the roles of transport fluxes in the momentum equation. It is shown that the ambipolar state is reached when the momentum equation is relaxed. It is also shown that the origin of the momentum for Plasma flow generated without momentum sources is the local unbalance of particles' momenta and is diamagnetic in nature regardless of the details of the theory.
S. A. Sabbagh - One of the best experts on this subject based on the ideXlab platform.
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neoclassical toroidal Plasma Viscosity with effects of finite banana width for finite aspect ratio tokamaks
Physics of Plasmas, 2016Co-Authors: K C Shaing, S. A. SabbaghAbstract:Theory for neoclassical toroidal Plasma Viscosity has been developed to model transport phenomena, especially, toroidal Plasma rotation for tokamaks with broken symmetry. Theoretical predictions are in agreement with the results of the numerical codes in the large aspect ratio limit. The theory has since been extended to include effects of finite aspect ratio and finite Plasma β. Here, β is the ratio of the Plasma thermal pressure to the magnetic field pressure. However, there are cases where the radial wavelength of the self-consistent perturbed magnetic field strength B on the perturbed magnetic surface is comparable to the width of the trapped particles, i.e., bananas. To accommodate those cases, the theory for neoclassical toroidal Plasma Viscosity is further extended here to include the effects of the finite banana width. The extended theory is developed using the orbit averaged drift kinetic equation in the low collisionality regimes. The results of the theory can now be used to model Plasma transpo...
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neoclassical Plasma Viscosity and transport processes in non axisymmetric tori
Nuclear Fusion, 2015Co-Authors: K C Shaing, K Ida, S. A. SabbaghAbstract:Neoclassical transport processes are important to the understanding of Plasma confinement physics in doubly periodic magnetized toroidal Plasmas, especially, after the impact of the momentum confinement on the particle and energy confinement is recognized. Real doubly periodic tori in general are non-axisymmetric, with symmetric tori as a special case. An eight-moment approach to transport theory with Plasma density N, Plasma pressure p, mass flow velocity V and heat flow q as independent variables is adopted. Transport processes are dictated by the solutions of the momentum and heat flux balance equations. For toroidal Plasma confinement devices, the first order (in the gyro-radius ordering) Plasma flows are on the magnetic surface to guarantee good Plasma confinement and are thus two-dimensional. Two linearly independent components of the momentum equation are required to determine the flows completely. Once this two-dimensional flow is relaxed, i.e. the momentum equation reaches a steady state, Plasmas become ambipolar, and all the transport fluxes are determined through the flux–force relation. The flux–force relation is derived both from the kinetic definitions for the transport fluxes and from the manipulation of the momentum and heat flux balance equations to illustrate the nature of the transport fluxes by examining their corresponding driven forces and their roles in the momentum and heat flux balance equations. Steady-state Plasma flows are determined by the components of the stress and heat stress tensors in the momentum and heat flux balance equations. This approach emphasizes the pivotal role of the momentum equation in the transport processes and is particularly useful in modelling Plasma flows in experiments. The methodology for neoclassical transport theory is applied to fluctuation-driven transport fluxes in the quasilinear theory to unify these two theories. Experimental observations in tokamaks and stellarators for the physics discussed are presented.
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theory for neoclassical toroidal Plasma Viscosity in tokamaks
Plasma Physics and Controlled Fusion, 2012Co-Authors: S. A. Sabbagh, C T Hsu, M S Chu, K C Shaing, Jae Chun Seol, Y SunAbstract:Error fields and magnetohydrodynamic modes break toroidal symmetry in tokamaks. The broken symmetry enhances the toroidal Plasma Viscosity, which results in a steady-state toroidal Plasma flow. A theory for neoclassical toroidal Plasma Viscosity in the low-collisionality regimes is developed. It extends stellarator transport theory to include multiple modes and to allow for |m???nq|???1. Here, m is the poloidal mode number, n is the toroidal mode number and q is the safety factor. The bounce averaged drift kinetic equation is solved in several asymptotic limits to obtain transport fluxes. These fluxes depend non-linearly on the radial electric field except for those in the 1/? regime. Here, ? is the collision frequency. The theory is refined to include the effects of the superbanana plateau resonance at the phase space boundary and the finite ?B drift on the collisional boundary layer fluxes. Analytical expressions that connect all asymptotic limits are constructed and are in good agreement with the numerical results. The flux?force relations that relate transport fluxes to forces are used to illustrate the roles of transport fluxes in the momentum equation. It is shown that the ambipolar state is reached when the momentum equation is relaxed. It is also shown that the origin of the momentum for Plasma flow generated without momentum sources is the local unbalance of particles' momenta and is diamagnetic in nature regardless of the details of the theory.
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superbanana plateau resonance in the vicinity of the phase space boundary in tokamaks
Nuclear Fusion, 2011Co-Authors: K C Shaing, M S Chu, T H Tsai, Y Sun, S. A. SabbaghAbstract:A theory for the superbanana plateau resonance that occurs at the phase space boundary is presented to refine the comprehensive theory for neoclassical toroidal Plasma Viscosity in tokamaks. The results of the theory reproduce those of the standard superbanana plateau resonance theory when the resonance occurs away from the boundary. It shows that the strength of the superbanana plateau resonance weakens in the vicinity of the phase space boundary. It also indicates that it is important to know the resonance pitch angle parameter when comparing the results of the superbanana plateau resonance with those of the experiments. The theory is used to refine the kernel for the superbanana plateau resonance in the approximate expression for the neoclassical toroidal Plasma Viscosity.
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theory for island induced neoclassical toroidal Plasma Viscosity in tokamaks
Nuclear Fusion, 2011Co-Authors: K C Shaing, M S Chu, T H Tsai, S. A. SabbaghAbstract:Error fields and resistive magnetohydrodynamic modes are ubiquitous in real tokamaks. They break the toroidal symmetry in |B| in tokamaks. Here, B is the magnetic field. There are two mechanisms that break the symmetry on the perturbed magnetic surface: one is the perturbed field itself and the other results from the distortion of the magnetic surface due to the perturbed field. The broken toroidal symmetry leads to enhanced neoclassical toroidal Plasma Viscosity and consequently the rate of the toroidal flow damping. The neoclassical toroidal Plasma Viscosity also results in a steady-state toroidal Plasma flow. In addition, the neoclassical toroidal Plasma Viscosity in the vicinity of the magnetic islands provides a mechanism to determine the island rotation frequency, which is an important quantity for the island stability. Here, the theory for neoclassical toroidal Plasma Viscosity in the vicinity of the magnetic island is extended to include the effects of the collisional boundary layer that lead to scaling in the transport fluxes, where ? is the collision frequency.
M S Chu - One of the best experts on this subject based on the ideXlab platform.
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theory for neoclassical toroidal Plasma Viscosity in tokamaks
Plasma Physics and Controlled Fusion, 2012Co-Authors: S. A. Sabbagh, C T Hsu, M S Chu, K C Shaing, Jae Chun Seol, Y SunAbstract:Error fields and magnetohydrodynamic modes break toroidal symmetry in tokamaks. The broken symmetry enhances the toroidal Plasma Viscosity, which results in a steady-state toroidal Plasma flow. A theory for neoclassical toroidal Plasma Viscosity in the low-collisionality regimes is developed. It extends stellarator transport theory to include multiple modes and to allow for |m???nq|???1. Here, m is the poloidal mode number, n is the toroidal mode number and q is the safety factor. The bounce averaged drift kinetic equation is solved in several asymptotic limits to obtain transport fluxes. These fluxes depend non-linearly on the radial electric field except for those in the 1/? regime. Here, ? is the collision frequency. The theory is refined to include the effects of the superbanana plateau resonance at the phase space boundary and the finite ?B drift on the collisional boundary layer fluxes. Analytical expressions that connect all asymptotic limits are constructed and are in good agreement with the numerical results. The flux?force relations that relate transport fluxes to forces are used to illustrate the roles of transport fluxes in the momentum equation. It is shown that the ambipolar state is reached when the momentum equation is relaxed. It is also shown that the origin of the momentum for Plasma flow generated without momentum sources is the local unbalance of particles' momenta and is diamagnetic in nature regardless of the details of the theory.
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superbanana plateau resonance in the vicinity of the phase space boundary in tokamaks
Nuclear Fusion, 2011Co-Authors: K C Shaing, M S Chu, T H Tsai, Y Sun, S. A. SabbaghAbstract:A theory for the superbanana plateau resonance that occurs at the phase space boundary is presented to refine the comprehensive theory for neoclassical toroidal Plasma Viscosity in tokamaks. The results of the theory reproduce those of the standard superbanana plateau resonance theory when the resonance occurs away from the boundary. It shows that the strength of the superbanana plateau resonance weakens in the vicinity of the phase space boundary. It also indicates that it is important to know the resonance pitch angle parameter when comparing the results of the superbanana plateau resonance with those of the experiments. The theory is used to refine the kernel for the superbanana plateau resonance in the approximate expression for the neoclassical toroidal Plasma Viscosity.
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theory for island induced neoclassical toroidal Plasma Viscosity in tokamaks
Nuclear Fusion, 2011Co-Authors: K C Shaing, M S Chu, T H Tsai, S. A. SabbaghAbstract:Error fields and resistive magnetohydrodynamic modes are ubiquitous in real tokamaks. They break the toroidal symmetry in |B| in tokamaks. Here, B is the magnetic field. There are two mechanisms that break the symmetry on the perturbed magnetic surface: one is the perturbed field itself and the other results from the distortion of the magnetic surface due to the perturbed field. The broken toroidal symmetry leads to enhanced neoclassical toroidal Plasma Viscosity and consequently the rate of the toroidal flow damping. The neoclassical toroidal Plasma Viscosity also results in a steady-state toroidal Plasma flow. In addition, the neoclassical toroidal Plasma Viscosity in the vicinity of the magnetic islands provides a mechanism to determine the island rotation frequency, which is an important quantity for the island stability. Here, the theory for neoclassical toroidal Plasma Viscosity in the vicinity of the magnetic island is extended to include the effects of the collisional boundary layer that lead to scaling in the transport fluxes, where ? is the collision frequency.
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an approximate analytic expression for neoclassical toroidal Plasma Viscosity in tokamaks
Nuclear Fusion, 2010Co-Authors: S. A. Sabbagh, Ker-chung Shaing, M S ChuAbstract:An approximate analytic expression for neoclassical toroidal Plasma Viscosity in tokamaks that have error fields or magnetohydrodynamic activities is presented. The expression smoothly joins transport fluxes or Plasma Viscosity in all the known collisionality regimes derived from the solution of the bounce averaged drift kinetic equation and should be useful in modelling results of existing and future tokamak experiments. It also incorporates some of the extensions of the known expressions to include the effects of finite ∇B drift in the non-resonant transport processes. Here, B is the magnitude of the magnetic field. The toroidal momentum balance equation is a nonlinear function of the radial electric field when the neoclassical Plasma Viscosity is dominant. It can have bifurcated solutions for the radial electric field and may lead to better Plasma confinement as a result.
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eulerian approach to bounce transit and drift resonance and neoclassical toroidal Plasma Viscosity in tokamaks
Plasma Physics and Controlled Fusion, 2009Co-Authors: K C Shaing, M S Chu, S. A. SabbaghAbstract:An Eulerian approach to treat the bounce–transit and precession drift resonance in tokamaks is developed by expanding the poloidal angle dependence in terms of a Jacobian elliptic function in the low collisionality regime instead of integrating along the unperturbed particle trajectories. One of the advantages is that a complex Coulomb collision operator can be adopted in the approach. The full thermodynamic forces are kept to conserve momentum in the collision processes. To illustrate the method, the approach is applied to calculate the neoclassical toroidal Plasma Viscosity in both the resonant plateau regime and the Pfirsch–Schluter regime. Both trapped particles and circulating particles contribute to the resonant plateau regime through the bounce and drift resonance and the transit and drift resonance, respectively. The dependences on Plasma parameters for both regimes are found to be the same as that of the nonlinear Plasma Viscosity. The resonant plateau regime naturally connects to the Pfirsch–Schluter regime in the collisional limit.
Marcos Intaglietta - One of the best experts on this subject based on the ideXlab platform.
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cardiovascular benefits in moderate increases of blood and Plasma Viscosity surpass those associated with lowering Viscosity experimental and clinical evidence
Clinical Hemorheology and Microcirculation, 2010Co-Authors: B Salazar Y Vazquez, Pedro Cabrales, Judith Martini, Chavez A Negrete, A G Tsai, Sandro Forconi, Paul C Johnson, Marcos IntagliettaAbstract:Decreasing blood Viscosity has been proposed since the advent of hemodilution as a means for increasing perfusion in many pathological conditions, and increased Plasma Viscosity is associated with the presence of pathological conditions. However, experimental studies show that microvascular functions as represented by functional capillary density in conditions of significantly decreased Viscosity is impaired, a problem corrected by increasing Plasma and blood Viscosity. Blood Viscosity, primarily dependent on hematocrit (Hct) is a determinant of peripheral vascular resistance, and therefore blood pressure. In the healthy population Hct presents a variability, which is not reflected by the variability of blood pressure. This is due to a regulatory process at the level of the endothelium, whereby the increase of Hct (and therefore blood Viscosity) leads to increased shear stress and the production of the vasodilator nitric oxide (NO), a finding supported by experimental studies showing that the acute increase of Hct lowers blood pressure. Studies that in the healthy population show that blood pressure and Hct have a weak positive correlation. However, when the effect of blood Viscosity is factored out, blood pressure and Hct are negatively and significantly correlated, indicating that as blood Viscosity increases, the circulation dilates. Conversely, lower Hct and blood Viscosity conditions lead to a constricted circulation, associated with a condition of decreased NO bioavailability, and therefore a pro-inflammatory condition.
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microvascular benefits of increasing Plasma Viscosity and maintaining blood Viscosity counterintuitive experimental findings
Biorheology, 2009Co-Authors: B Salazar Y Vazquez, Pedro Cabrales, Judith Martini, Chavez A Negrete, A G Tsai, Marcos IntagliettaAbstract:The circulation is adapted to specific levels of blood Viscosity resulting in a balance that simultaneously sets peripheral vascular resistance, blood pressure and cardiac output, factors in part mediated by the production of nitric oxide by the endothelium. Although it is generally perceived that decreasing blood Viscosity is beneficial for cardiovascular function, small increases of blood Viscosity in normal healthy experimental subjects significantly improve cardiovascular function. These changes are within the normal variations of Viscosity due to the variations of hematocrit in the healthy population. Hemodilution reduces blood Viscosity, which is proposed to be physiologically beneficial. However, in extreme hemodilution, increased Plasma Viscosity via the use of viscogenic Plasma expanders sustains microvascular and tissue function at significantly reduced levels of oxygen delivery. Studies in hemorrhagic shock resuscitation using oxygen carrying and non-carrying red blood cells show that restoration of blood Viscosity is as important as restoration of oxygen carrying capacity. It is concluded that although hemodilution is indicated for reducing abnormally high blood viscosities, it is beneficial to increase Plasma Viscosity when hematocrit is reduced. Furthermore small increases in hematocrit may be beneficial due to the related increase in blood Viscosity, independently of the increase of oxygen delivery capacity.
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increased Plasma Viscosity prolongs microhemodynamic conditions during small volume resuscitation from hemorrhagic shock
Resuscitation, 2008Co-Authors: Pedro Cabrales, Amy G Tsai, Marcos IntagliettaAbstract:Summary Systemic and microvascular hemodynamic responses to hemorrhagic shock resuscitation with hypertonic saline (HTS, 7.5% NaCl) followed with a small volume of Plasma expander were studied in the hamster window chamber model to determine the role of Plasma expander Viscosity in the acute resuscitation outcome. Moderate hemorrhagic shock was induced by arterial controlled bleeding of 50% of blood volume (BV) and the hypovolemic state was maintained for 1 h. Volume restitution was performed by infusion of HTS, 3.5% of BV followed by 10% of BV Plasma expanders. Resuscitation was followed for 90 min. The experimental groups were named based on the Plasma expanders infused after the HTS, namely: [ Hextend ], Hextend ® (6% Hetastarch 670 kDa in lactated electrolyte solution, 4 cp), [ Hextend+V ], Hextend ® with Viscosity enhanced by the addition of 0.4% alginate, 8 cp, and [ NVR ] no volume resuscitation as control group. Measurement of systemic parameters, microvascular hemodynamics and capillary perfusion were performed during hemorrhage, shock and resuscitation. Restitution with Hextend yielded the higher mean arterial pressure (MAP), followed by Hextend+V and NVR . Increasing Plasma Viscosity did not increase peripheral vascular resistance. Functional capillary density (FCD) was higher for Hextend+V than Hextend and NVR . The level of restoration of acid–base balance correlated with microvascular perfusion and was significantly improved with Hextend+V when compared to Hextend and NVR . These results suggest the importance of restoration of blood rheological properties through enhancing Plasma Viscosity, influencing the re-establishment of microvascular perfusion during small volume resuscitation from hemorrhagic shock.
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beneficial effects due to increasing blood and Plasma Viscosity
Clinical Hemorheology and Microcirculation, 2006Co-Authors: Judith Martini, Pedro Cabrales, Chavez A Negrete, A G Tsai, B Carpentier, Marcos IntagliettaAbstract:Increased Plasma and blood Viscosity are usually associated with pathological conditions; however there are several situations in which the elevation of both parameters results in increased perfusion and the lowering of peripheral vascular resistance. In extreme hemodilution blood Viscosity is too low and insufficient to maintain functional capillary density, a problem that in experimental studies is shown to be corrected by increasing Plasma Viscosity up to 2.2 cP. This effect is mediated by Nitric oxide (NO) production via restoration of shear stress at the endothelium as shown by microelectrode perivascular measurements of NO concentration. Moderate elevations of blood Viscosity by increasing hematocrit (approximately 10% of baseline) result in reductions of blood pressure by 10 mmHg of baseline. This effect is also NO mediated since it is absent after N-nitro-L-arginine methyl ester (L-NAME) treatment and in endothelial NO synthase deficient mice. These results show that the rheological properties of Plasma affect vessel diameter in the microcirculation leading to counterintuitive responses to the increase in Viscosity.
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alginate Plasma expander maintains perfusion and Plasma Viscosity during extreme hemodilution
American Journal of Physiology-heart and Circulatory Physiology, 2005Co-Authors: Pedro Cabrales, Amy G Tsai, Marcos IntagliettaAbstract:Extreme hemodilution was performed in the hamster chamber window model using 6% Dextran 70, lowering systemic hematocrit by 60%. Animals were subsequently divided into three groups and hemodiluted ...
Ker-chung Shaing - One of the best experts on this subject based on the ideXlab platform.
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Intrinsic Plasma rotation determined by neoclassical toroidal Plasma Viscosity in tokamaks
Nuclear Fusion, 2013Co-Authors: Youwen Sun, Ker-chung Shaing, Y Liang, T.a. Casper, A. Loarte, Biao Shen, Baonian WanAbstract:Intrinsic toroidal Plasma rotation due to the neoclassical toroidal Plasma Viscosity (NTV) effect induced by a three-dimensional helical magnetic field ripple in tokamaks is investigated in this paper. The intrinsic rotation is determined self-consistently by searching for the roots of the ambipolarity constraint, after evaluation of the particle fluxes from the numerical modelling. In the low-collisionality case, there are three roots, in which two are stable roots. One corresponds to the ?ion root? in the counter-current direction, and the other stable one corresponds to the ?electron root? in the co-current direction, near which the electron flux is dominant. Both of the two stable roots scale like the diamagnetic frequency. In the high-collisionality case, there is only one ?ion? root. The application of this modelling for International Thermonuclear Experimental Reactor (ITER) cases is discussed. In a large range of Plasma radii, there are three roots. The NTV torque drives Plasma rotation in ITER towards one of the stable roots, depending on the initial condition. The amplitudes of the electron roots near the pedestal in both baseline and steady-state scenarios are much larger than that of the ion roots. The amplitudes of the NTV torque density and the electron roots near the pedestal increase with increasing height of the temperature pedestal in the ITER baseline scenario.
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an approximate analytic expression for neoclassical toroidal Plasma Viscosity in tokamaks
Nuclear Fusion, 2010Co-Authors: S. A. Sabbagh, Ker-chung Shaing, M S ChuAbstract:An approximate analytic expression for neoclassical toroidal Plasma Viscosity in tokamaks that have error fields or magnetohydrodynamic activities is presented. The expression smoothly joins transport fluxes or Plasma Viscosity in all the known collisionality regimes derived from the solution of the bounce averaged drift kinetic equation and should be useful in modelling results of existing and future tokamak experiments. It also incorporates some of the extensions of the known expressions to include the effects of finite ∇B drift in the non-resonant transport processes. Here, B is the magnitude of the magnetic field. The toroidal momentum balance equation is a nonlinear function of the radial electric field when the neoclassical Plasma Viscosity is dominant. It can have bifurcated solutions for the radial electric field and may lead to better Plasma confinement as a result.
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Collisional boundary layer analysis for neoclassical toroidal Plasma Viscosity in tokamaks
Physics of Plasmas, 2008Co-Authors: Ker-chung Shaing, M. Becoulet, P. Cahyna, Jong Kyu Park, S. A. SabbaghAbstract:It is demonstrated that the pitch angle integrals in the transport fluxes in the ν regime calculated in K. C. Shang [Phys. Plasmas 10, 1443 (2003)] are divergent as the trapped-circulating boundary is approached. Here, ν is the collision frequency. The origin of this divergence results from the logarithmic dependence in the bounce averaged radial drift velocity. A collisional boundary layer analysis is developed to remove the singularity. The resultant pitch angle integrals now include not only the original physics of the ν regime but also the boundary layer physics. The transport fluxes, caused by the particles inside the boundary layer, scale as ν.
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Effects of orbit squeezing on neoclassical toroidal Plasma Viscosity in tokamaks
Physics of Plasmas, 2008Co-Authors: Ker-chung Shaing, M. Becoulet, S. A. Sabbagh, P. CahynaAbstract:The effects of orbit squeezing are important to neoclassical and anomalous transport fluxes in the region where Plasma confinement is improved. This occurs in the edge region after the transition from the low confinement mode (L-mode) to the high confinement mode (H-mode) or in the vicinity of low-order rational surfaces. Neoclassical toroidal Viscosity in tokamaks induced by the broken toroidal symmetry resulting from the activity of magnetohydrodynamic instabilities or error fields is calculated to include orbit squeezing effects. It is found that in the 1∕ν regime, the magnitude of the neoclassical toroidal Viscosity is enhanced by a factor of ∣S∣3∕2, where ν is the collision frequency and S is the orbit squeezing factor; while in the ν regime, it is reduced by a factor of ∣S∣1∕2. A boundary layer analysis is performed to remove the singularity in the vicinity of the trapped-circulating boundary in the ν regime. As a result, the well-known ν regime is recovered. Orbit squeezing has little effect in the...