5.1 Formation and structure of collisionless shocks
3 min read•july 31, 2024
Collisionless shocks in space plasmas form when plasma regions move faster than local wave speeds. Without particle collisions, energy dissipates through magnetic field compression and particle reflection. These shocks play a key role in solar wind interactions with planets.
Shock structure includes abrupt changes in plasma properties across a thin transition region. Characteristics vary based on the angle between the magnetic field and shock normal. Microstructures like the foot, ramp, and overshoot regions develop, shaping the complex shock environment.
Collisionless Shocks in Space Plasmas
Formation Mechanisms
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- Collisionless shocks form when relative speed between two plasma regions exceeds local speed of sound or magnetosonic wave speed
- Absence of particle collisions requires alternative mechanisms for energy dissipation and entropy increase
- Magnetic field compression
- Particle reflection
- Critical Mach number determines threshold for shock transition in collisionless plasma
- Nonlinear and instabilities contribute to shock front development
- Primary sources in solar system
- Solar wind interaction with planetary magnetospheres (Earth's bow shock)
- Interplanetary magnetic field discontinuities (interplanetary shocks)
Physical Processes
- Magnetic field compression plays crucial role in magnetized plasmas
- Compresses and aligns magnetic field lines
- Increases magnetic field strength across shock
- Particle reflection contributes to energy dissipation
- Ions reflected off shock potential
- Creates population of energetic particles upstream
- Wave-particle interactions facilitate energy transfer
- Generates electromagnetic waves (whistler waves)
- Scatters particles in velocity space
- Plasma instabilities develop at shock front
- Two-stream instability from reflected particles
- Mirror instability from temperature anisotropy
Structure of Collisionless Shocks
Shock Characteristics
- Abrupt changes in plasma parameters across shock front
- Density increases
- Temperature rises
- Magnetic field strength jumps
- Flow velocity decreases
- Shock transition region
- Thin layer where bulk plasma deceleration and heating occurs
- Thickness on order of ion inertial length or ion gyroradius
- Shock classification based on angle between upstream magnetic field and shock normal
- Quasi-perpendicular shocks (angle > 45°)
- Quasi-parallel shocks (angle < 45°)
- Rankine-Hugoniot jump conditions describe relationship between upstream and downstream plasma parameters
- Conservation of mass, momentum, and energy
- , ,
- Shock strength characterized by Mach number
- Ratio of upstream flow speed to relevant wave speed
- (Alfvénic Mach number)
Microstructures
- Foot region in quasi-perpendicular shocks
- Formed by gyrating ions reflected from shock front
- Extends upstream for distance of ion gyroradius
- Ramp
- Main transition layer with significant changes in plasma parameters
- Thickness of few electron inertial lengths
- Overshoot region in supercritical shocks
- Magnetic field magnitude exceeds downstream asymptotic value
- Result of ion reflection and gyration
- Turbulent downstream region
- Heated and compressed plasma
- Reduced flow velocity relative to shock front
- Quasi-parallel shock structures
- Extended foreshock regions with complex wave-particle interactions
- Large-amplitude magnetic fluctuations
- Series of pulsations rather than well-defined single ramp
Regions and Layers of Collisionless Shocks
Upstream Region
- Undisturbed plasma flow
- Presence of backstreaming particles
- Reflected ions (field-aligned beams)
- Energetic electrons
- Wave generation by shock-reflected particles
- Ultra-low frequency waves (ULF waves)
- Whistler waves
- Foreshock region in quasi-parallel shocks
- Extended area of particle-wave interactions
- Diffuse ion populations
- Steepened magnetic structures (SLAMS)
Transition Region
- Foot region in quasi-perpendicular shocks
- Gyrating ions create magnetic field increase
- Thickness proportional to ion gyroradius
- Ramp
- Steepest gradient in magnetic field and plasma parameters
- Electric field spikes
- Electron heating through microinstabilities
- Overshoot
- Magnetic field peak exceeding downstream value
- Ion reflection and gyration contribute to overshoot formation
- Quasi-parallel shock transition
- Series of large-amplitude pulsations
- Cyclic reformation process
- Intermittent particle reflection and transmission
Downstream Region
- Turbulent, heated, and compressed plasma
- Reduced flow velocity relative to shock front
- Magnetic field fluctuations
- Mirror mode waves in high-beta plasma
- Alfvén waves
- Particle distributions
- Thermalized ion populations
- Suprathermal electron tails
- Gradual relaxation to asymptotic downstream state
- Decay of shock-generated waves
- Isotropization of particle distributions
Key Terms to Review (17)
David Burgess: David Burgess is a prominent researcher known for his work in the field of space physics, particularly in the study of collisionless shocks. His contributions help to deepen the understanding of how these shocks form and their structure, which is crucial for comprehending various astrophysical phenomena, including cosmic rays and solar wind interactions.
Dispersive Wave: A dispersive wave is a wave whose speed varies depending on its frequency or wavelength, causing different frequency components to travel at different velocities. This phenomenon leads to the spreading out of a wave packet over time, which is crucial for understanding the behavior of waves in various media, including in collisionless shocks. In the context of collisionless shocks, dispersive waves play a key role in the dynamics and interactions of plasma particles as they respond to changing electromagnetic fields.
Fluid Dynamics: Fluid dynamics is the study of the behavior of fluids (liquids and gases) in motion. It is crucial for understanding various phenomena, including the movement of plasma in space, which plays a significant role in processes like collisionless shocks and overall space physics. Fluid dynamics incorporates principles from physics and mathematics to analyze how forces affect fluid flow, which helps to explain complex interactions within different systems in space.
Hannes Alfvén: Hannes Alfvén was a Swedish physicist known for his pioneering work in plasma physics and magnetohydrodynamics, significantly contributing to our understanding of space phenomena. His theories laid the foundation for the study of plasma behavior in cosmic environments, linking magnetic fields and electrically charged particles, which is crucial for understanding various space physics concepts.
Hydrodynamic models: Hydrodynamic models are mathematical frameworks used to describe the flow and behavior of fluids, often applied to astrophysical contexts like collisionless shocks. These models help in understanding how plasma behaves under different conditions, such as compressibility, viscosity, and external forces, allowing scientists to predict the evolution and structure of shock waves in space environments.
Ionization: Ionization is the process in which an atom or molecule gains or loses electrons, resulting in the formation of charged particles known as ions. This process is crucial in understanding the behavior of plasmas, as ionization leads to the creation of a collection of free electrons and ions that can interact electromagnetically, influencing phenomena like collisions and electromagnetic fields.
Kinetic Theory: Kinetic theory describes how the behavior of particles in matter relates to temperature and pressure, providing a statistical understanding of the properties of gases, liquids, and plasmas. This theory is fundamental in explaining phenomena such as plasma waves, instabilities, and the behavior of charged particles in various space environments.
Magnetic Reconnection: Magnetic reconnection is a physical process in plasma physics where magnetic field lines rearrange and release energy, often occurring in the presence of highly conducting plasmas. This process plays a crucial role in the dynamics of solar flares, coronal mass ejections, and the behavior of the Earth's magnetosphere, linking various phenomena in space environments.
Magnetosonic shock: A magnetosonic shock is a type of wave that occurs in a magnetized plasma, combining features of both sonic and magnetic waves. It forms when the plasma flow exceeds the speed of sound in that medium while also interacting with magnetic fields, creating a transition layer that separates regions of different plasma properties. This phenomenon is significant in understanding how energy and momentum transfer occurs in collisionless shocks, especially in astrophysical contexts like solar winds and planetary magnetospheres.
Maxwell Equations: Maxwell's equations are a set of four fundamental equations that describe how electric and magnetic fields interact and propagate in space and time. These equations form the foundation of classical electromagnetism, governing the behavior of electromagnetic waves, including light, and play a critical role in understanding various astrophysical phenomena, including collisionless shocks.
Nonlinear landau damping: Nonlinear Landau damping refers to a mechanism in plasma physics where wave-particle interactions lead to the decay of wave amplitudes over time due to the redistribution of particles in velocity space. This phenomenon is particularly significant in collisionless plasmas, where it plays a crucial role in the formation and structure of collisionless shocks, as it contributes to energy dissipation and the stabilization of shock waves through nonlinear effects.
Particle acceleration: Particle acceleration refers to the process by which charged particles, such as electrons and ions, gain kinetic energy and increase their speed due to electromagnetic forces. This process plays a critical role in various astrophysical phenomena, influencing the dynamics of shock waves, magnetic field interactions, energy transfer in the magnetosphere, and the release of energy during space weather events.
Phase Space: Phase space is a mathematical concept that represents all possible states of a system, characterized by the positions and momenta of its particles. It is crucial for understanding the dynamics of systems, including plasma waves and collisionless shocks, as it helps visualize how particles evolve over time and how different states are interconnected.
Solar wind shock: A solar wind shock is a type of shock wave created when the high-speed solar wind emitted by the Sun encounters obstacles in space, such as the Earth's magnetosphere. This interaction results in a rapid change in plasma conditions and is a key feature of collisionless shocks that can affect space weather and satellite operations. Solar wind shocks are critical for understanding how solar activity influences the near-Earth environment and the structure of the heliosphere.
Thermalization: Thermalization is the process by which a system reaches thermal equilibrium, where its temperature becomes uniform and energy is distributed among its particles in a balanced manner. In astrophysical contexts, especially in collisionless shocks, thermalization is crucial as it dictates how energy from shock waves is transferred to particles, resulting in heating and acceleration.
Vlasov Equation: The Vlasov Equation describes the evolution of the distribution function of particles in a plasma under the influence of electric and magnetic fields, without accounting for collisions. This equation is fundamental in kinetic theory, enabling the study of plasma waves, the behavior of charged particles in collisionless environments, and serves as a foundation for understanding complex plasma phenomena such as shocks.
Wave Steepening: Wave steepening refers to the phenomenon where the slope of a wave increases as it propagates, leading to a sharper peak or crest. This occurs due to the nonlinear effects in wave dynamics, particularly in plasma and fluid systems, where the wave's energy concentrates at the crest, causing changes in its shape. Wave steepening is a crucial concept in understanding the formation and structure of collisionless shocks, where energy dissipation and particle acceleration play significant roles.