9.3 Intermediate shocks and rotational discontinuities
4 min read•august 16, 2024
and are crucial MHD structures in space plasmas. They differ in how they change plasma properties and magnetic fields, playing key roles in energy transfer and magnetic topology changes.
Intermediate shocks transition flow from super- to sub-Alfvénic, changing field magnitude and plasma density. Rotational discontinuities only rotate the magnetic field, preserving its magnitude and plasma properties. Both are important in magnetic reconnection and space plasma dynamics.
Intermediate Shocks vs Rotational Discontinuities
Definitions and Key Characteristics
Top images from around the web for Definitions and Key Characteristics
Harmonic Magnetic Dipole — Electromagnetic Geophysics View original
Is this image relevant?
9.3 Earth’s Magnetic Field | Physical Geology View original
Is this image relevant?
Gauss’s Law for Magnetic Fields — Electromagnetic Geophysics View original
Is this image relevant?
Harmonic Magnetic Dipole — Electromagnetic Geophysics View original
Is this image relevant?
9.3 Earth’s Magnetic Field | Physical Geology View original
Is this image relevant?
1 of 3
Top images from around the web for Definitions and Key Characteristics
Harmonic Magnetic Dipole — Electromagnetic Geophysics View original
Is this image relevant?
9.3 Earth’s Magnetic Field | Physical Geology View original
Is this image relevant?
Gauss’s Law for Magnetic Fields — Electromagnetic Geophysics View original
Is this image relevant?
Harmonic Magnetic Dipole — Electromagnetic Geophysics View original
Is this image relevant?
9.3 Earth’s Magnetic Field | Physical Geology View original
Is this image relevant?
1 of 3
Intermediate shocks involve changes in tangential magnetic field component and transition from super-Alfvénic to sub-Alfvénic flow
Rotational discontinuities rotate magnetic field vector without changing magnitude or plasma density
Both structures manifest as non-linear wave structures in magnetized plasmas
Intermediate shocks classified based on normal flow velocity changes relative to characteristic MHD speeds (fast, intermediate, slow)
Rotational discontinuities propagate at Alfvén speed maintaining constant normal components of magnetic field and velocity
These structures play crucial roles in energy transfer and magnetic field topology changes in space plasmas (solar wind, magnetosphere)
Classification and Propagation
Intermediate shocks types determined by relationship between upstream and downstream flow speeds and characteristic MHD wave speeds
Slow-intermediate shocks: upstream flow super-slow and sub-intermediate, downstream flow sub-slow
Fast-intermediate shocks: upstream flow super-fast, downstream flow sub-intermediate and super-slow
Rotational discontinuities always propagate at local Alfvén speed vA=B/μ0ρ where B is magnetic field strength and ρ is plasma density
Intermediate shock propagation speed varies depending on type and plasma parameters
Generally between slow and fast magnetosonic speeds
Rotational discontinuities maintain constant propagation speed in homogeneous plasma
Properties of Shocks vs Discontinuities
Plasma Parameter Changes
Intermediate shocks change plasma density and pressure
Density increases across shock front
Pressure rises due to compression and heating
Rotational discontinuities maintain constant density and pressure
Both rotate magnetic field, but intermediate shocks also change field magnitude
Intermediate shocks compress plasma and produce entropy
Rotational discontinuities remain non-compressive and isentropic
Intermediate shocks can convert between MHD wave modes (Alfvén to magnetosonic)
Intermediate shocks require sufficiently high plasma beta β=B22μ0p
Allows necessary compression and magnetic field changes
Typically β>1 for intermediate shock formation
Incident flow must be super-Alfvénic for at least one characteristic MHD wave speed
Ensures shock formation through nonlinear steepening
Rotational discontinuities exist in both high and low plasma beta regimes
No density or pressure changes required
Both structures need guide magnetic field component parallel to discontinuity surface
Enables rotation of field vector
Stability and Formation Mechanisms
Intermediate shock stability depends on balance between nonlinear steepening and dispersive effects
Steepening tends to sharpen shock front
Dispersion acts to spread out disturbance
Rotational discontinuities more readily formed in collisionless plasmas
Kinetic effects support field rotation without dissipation
Ion and electron dynamics crucial for maintaining structure
Intermediate shocks can form through nonlinear wave steepening or collision of simpler MHD discontinuities
Slow shocks merging with rotational discontinuities
Rotational discontinuities often result from large-amplitude Alfvén waves or magnetic field line draping
Solar wind interactions with planetary magnetospheres (Earth's magnetopause)
Key Terms to Review (18)
Astrophysical jets: Astrophysical jets are highly collimated streams of plasma that are ejected from the regions around astronomical objects such as black holes, neutron stars, and young stellar objects. These jets play a crucial role in transporting energy and matter across vast distances in space, influencing the surrounding environment and the evolution of galaxies.
C. f. f. l. de villeneuve: C. F. F. L. de Villeneuve is a concept related to the study of fluid dynamics and magnetohydrodynamics, particularly concerning the behavior of intermediate shocks and rotational discontinuities in compressible flows. This term emphasizes the role of specific transformations and equations that help describe the physical conditions and characteristics of such discontinuities within a flow field.
Characteristic Analysis: Characteristic analysis is a mathematical technique used to study the behavior of hyperbolic partial differential equations, particularly in fluid dynamics. This approach identifies characteristics, or curves along which information propagates, allowing us to understand complex flow patterns, including shocks and discontinuities, which are crucial in the analysis of fluid behavior under varying conditions.
Compression waves: Compression waves are a type of mechanical wave characterized by regions of high pressure (compressions) followed by regions of low pressure (rarefactions) as they propagate through a medium. These waves are fundamental in understanding how disturbances travel in fluids and plasmas, and they play a significant role in the dynamics of shocks and discontinuities.
Conservation Equations: Conservation equations are mathematical expressions that describe the principle of conservation of physical quantities such as mass, momentum, and energy in a fluid or plasma. These equations play a critical role in understanding the behavior of magnetohydrodynamic systems, especially when analyzing phenomena like intermediate shocks and rotational discontinuities, as they provide a framework for predicting how these quantities change across different regions in a flow.
Density Jump: A density jump refers to a sudden change in the density of a magnetohydrodynamic flow, typically occurring across a shock wave or discontinuity in the flow field. This phenomenon is crucial in understanding how fluid properties change in regions where there are abrupt transitions, affecting the overall dynamics of the flow and the behavior of magnetic fields within it.
Expansion Waves: Expansion waves are disturbances in a fluid that occur when the flow is accelerated to supersonic speeds, resulting in a decrease in pressure and density. These waves are critical in understanding the behavior of compressible flows and are especially significant in the context of intermediate shocks and rotational discontinuities, where they influence the characteristics of the flow field and can lead to complex interactions with other wave types.
H. alfvén: h. alfvén refers to Hannes Alfvén, a Swedish physicist known for his groundbreaking work in magnetohydrodynamics (MHD), particularly in the context of force-free magnetic fields and plasma physics. His contributions include the Alfvén wave, which describes how magnetic fields interact with conductive fluids, demonstrating the significance of magnetic forces in astrophysical phenomena and laboratory plasmas.
Ideal MHD: Ideal magnetohydrodynamics (MHD) is a theoretical framework that describes the behavior of electrically conducting fluids in the presence of magnetic fields, assuming that the effects of viscosity and resistivity are negligible. This approximation simplifies the governing equations, allowing for the analysis of plasma dynamics, where fluid motion is coupled with electromagnetic forces, leading to the formation of structures like shocks and waves.
Intermediate shocks: Intermediate shocks refer to a type of shock wave that forms in a magnetohydrodynamic (MHD) system, specifically in situations where the flow transitions between subsonic and supersonic states. These shocks can be characterized by their ability to maintain a level of rotationality, meaning that they can sustain the tangential velocity components while allowing for the transfer of energy and momentum across the shock front. Understanding intermediate shocks is crucial for analyzing the complex behavior of plasma in MHD flows and their influence on both shock structures and energy dissipation mechanisms.
Magnetic field line topology: Magnetic field line topology refers to the geometric arrangement and connectivity of magnetic field lines in a given space. This concept is crucial for understanding how magnetic fields interact with charged particles and plasmas, which is especially relevant in phenomena like intermediate shocks and rotational discontinuities, where the structure of magnetic fields can influence shock behavior and particle dynamics.
Non-ideal mhd: Non-ideal magnetohydrodynamics (MHD) refers to the study of plasma behavior that includes the effects of viscosity, thermal conduction, and electrical resistivity, distinguishing it from ideal MHD where such effects are neglected. This approach becomes crucial when examining real-world phenomena where these non-ideal factors significantly impact the dynamics of plasmas, especially in cases involving shocks and discontinuities in magnetic fields.
Pressure Gradient: A pressure gradient is a physical quantity that describes the rate of pressure change in a fluid with respect to distance. It plays a crucial role in driving fluid motion, as fluids tend to flow from areas of high pressure to areas of low pressure. Understanding this concept is essential for analyzing forces in magnetostatic equilibrium, the behavior of shocks and discontinuities, and fluid flows in ducts influenced by magnetic fields.
Rankine-Hugoniot Conditions: Rankine-Hugoniot conditions are mathematical relationships that describe the conservation of mass, momentum, and energy across a discontinuity in a flow field, such as a shock wave in magnetohydrodynamics. These conditions are crucial for understanding how different types of shocks, including intermediate shocks and fast or slow MHD shocks, behave and evolve. They help us analyze the changes in physical quantities like density, velocity, and pressure as fluid passes through these discontinuities.
Riemann Problem: The Riemann Problem refers to a type of initial value problem in hyperbolic partial differential equations, which specifically focuses on solving equations that model waves and shocks in various physical contexts. This problem is essential for understanding how discontinuities, such as shock waves and contact discontinuities, evolve over time in fluid dynamics, particularly in magnetohydrodynamics. The solutions to the Riemann Problem can reveal intermediate shocks and rotational discontinuities, which are crucial for analyzing complex flow patterns.
Rotational Discontinuities: Rotational discontinuities are specific types of magnetohydrodynamic (MHD) structures where there is a change in the flow velocity direction without any accompanying change in density or pressure. They occur when there is a rotation of the magnetic field and fluid flow, leading to a shift in the angular momentum while preserving the other fluid properties. This phenomenon is important for understanding how plasma behaves in various astrophysical and laboratory contexts, as it illustrates the complexity of magnetic fields interacting with conducting fluids.
Shock wave structure: Shock wave structure refers to the complex arrangement of physical changes that occur in a fluid as it passes through a shock wave, including changes in pressure, temperature, and density. This structure is crucial for understanding how shocks interact with different flow regimes and can lead to phenomena such as intermediate shocks and rotational discontinuities, where the properties of the flow are altered in distinctive ways.
Space Plasma Physics: Space plasma physics is the study of ionized gases (plasmas) in space, which are essential for understanding various cosmic phenomena and the behavior of charged particles in the universe. This field examines interactions between plasmas, magnetic fields, and electric fields, providing insights into the dynamics of astrophysical processes, including solar wind interactions with planetary atmospheres and magnetic fields.