Magnetohydrodynamics

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https://en.wikipedia.org/wiki/Magnetohydrodynamics

The plasma making up the Sun can be modeled as an MHD system

Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydro­magnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in numerous fields including geophysics, astrophysics, and engineering.

The word magneto­hydro­dynamics is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970.

History

The MHD description of electrically conducting fluids was first developed by Hannes Alfvén in a 1942 paper published in Nature titled "Existence of Electromagnetic–Hydrodynamic Waves" which outlined his discovery of what are now referred to as Alfvén waves. Alfvén initially referred to these waves as "electromagnetic–hydrodynamic waves"; however, in a later paper he noted, "As the term 'electromagnetic–hydrodynamic waves' is somewhat complicated, it may be convenient to call this phenomenon 'magneto–hydrodynamic' waves."

Equations

In MHD, motion in the fluid is described using linear combinations of the mean motions of the individual species: the current density $\mathbf{J}$ and the center of mass velocity $\mathbf{v}$. In a given fluid, each species $\sigma$ has a number density ${\displaystyle n_{\sigma }}$, mass ${\displaystyle m_{\sigma }}$, electric charge ${\displaystyle q_{\sigma }}$, and a mean velocity ${\displaystyle {\mathbf{u}}_{\sigma }}$. The fluid's total mass density is then $\rho =\sum _{\sigma }{m}_{\sigma }{n}_{\sigma }$, and the motion of the fluid can be described by the current density expressed as

${\displaystyle \mathbf{J}=\sum _{\sigma }{n}_{\sigma }{q}_{\sigma }{\mathbf{u}}_{\sigma }}$

and the center of mass velocity expressed as:

${\displaystyle \mathbf{v}=\frac{1}{\rho }\sum _{\sigma }{m}_{\sigma }{n}_{\sigma }{\mathbf{u}}_{\sigma }.}$

MHD can be described by a set of equations consisting of a continuity equation, an equation of motion, an equation of state, Ampère's Law, Faraday's law, and Ohm's law. As with any fluid description to a kinetic system, a closure approximation must be applied to highest moment of the particle distribution equation. This is often accomplished with approximations to the heat flux through a condition of adiabaticity or isothermality.

In the adiabatic limit, that is, the assumption of an isotropic pressure $p$ and isotropic temperature, a fluid with an adiabatic index $\gamma$, electrical resistivity $\eta$, magnetic field $\mathbf{B}$, and electric field $\mathbf{E}$ can be described by the continuity equation

${\displaystyle \frac{\mathrm{\partial }\rho }{\mathrm{\partial }t}+\mathrm{\nabla }\cdot \left(\rho \mathbf{v}\right)=0,}$

the equation of state

$\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{p}{{\rho }^{\gamma }}\right)=0,$

the equation of motion

${\displaystyle \rho \left(\frac{\mathrm{\partial }}{\mathrm{\partial }t}+\mathbf{v}\cdot \mathrm{\nabla }\right)\mathbf{v}=\mathbf{J}\times \mathbf{B}-\mathrm{\nabla }p,}$

the low-frequency Ampère's law

${\displaystyle {\mu }_0\mathbf{J}=\mathrm{\nabla }\times \mathbf{B},}$

Faraday's law

${\displaystyle \frac{\mathrm{\partial }\mathbf{B}}{\mathrm{\partial }t}=-\mathrm{\nabla }\times \mathbf{E},}$

and Ohm's law

${\displaystyle \mathbf{E}+\mathbf{v}\times \mathbf{B}=\eta \mathbf{J}.}$

Taking the curl of this equation and using Ampère's law and Faraday's law results in the induction equation,

${\displaystyle \frac{\mathrm{\partial }\mathbf{B}}{\mathrm{\partial }t}=\mathrm{\nabla }\times (\mathbf{v}\times \mathbf{B})+\frac{\eta }{{\mu }_0}{\mathrm{\nabla }}^2\mathbf{B},}$

where ${\displaystyle \eta /{\mu }_0}$ is the magnetic diffusivity.

In the equation of motion, the Lorentz force term $\mathbf{J}\times \mathbf{B}$ can be expanded using Ampère's law and a vector calculus identity to give

$\mathbf{J}\times \mathbf{B}=\frac{\left(\mathbf{B}\cdot \mathrm{\nabla }\right)\mathbf{B}}{{\mu }_0}-\mathrm{\nabla }\left(\frac{B^2}{2{\mu }_0}\right),$

where the first term on the right hand side is the magnetic tension force and the second term is the magnetic pressure force.

Ideal MHD

In view of the infinite conductivity, every motion (perpendicular to the field) of the liquid in relation to the lines of force is forbidden because it would give infinite eddy currents. Thus the matter of the liquid is "fastened" to the lines of force...

Hannes Alfvén, 1943

The simplest form of MHD, ideal MHD, assumes that the resistive term ${\displaystyle \eta \mathbf{J}}$ in Ohm's law is small relative to the other terms such that it can be taken to be equal to zero. This occurs in the limit of large magnetic Reynolds numbers during which magnetic induction dominates over magnetic diffusion at the velocity and length scales under consideration. Consequently, processes in ideal MHD that convert magnetic energy into kinetic energy, referred to as ideal processes, cannot generate heat and raise entropy.

A fundamental concept underlying ideal MHD is the frozen-in flux theorem which states that the bulk fluid and embedded magnetic field are constrained to move together such that one can be said to be "tied" or "frozen" to the other. Therefore, any two points that move with the bulk fluid velocity and lie on the same magnetic field line will continue to lie on the same field line even as the points are advected by fluid flows in the system. The connection between the fluid and magnetic field fixes the topology of the magnetic field in the fluid—for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid has negligible resistivity. This difficulty in reconnecting magnetic field lines makes it possible to store energy by moving the fluid or the source of the magnetic field. The energy can then become available if the conditions for ideal MHD break down, allowing magnetic reconnection that releases the stored energy from the magnetic field.

Ideal MHD equations

In ideal MHD, the resistive term ${\displaystyle \eta \mathbf{J}}$ vanishes in Ohm's law giving the ideal Ohm's law,

${\displaystyle \mathbf{E}+\mathbf{v}\times \mathbf{B}=0.}$

Similarly, the magnetic diffusion term ${\displaystyle \eta {\mathrm{\nabla }}^2\mathbf{B}/{\mu }_0}$ in the induction equation vanishes giving the ideal induction equation,

${\displaystyle \frac{\mathrm{\partial }\mathbf{B}}{\mathrm{\partial }t}=\mathrm{\nabla }\times (\mathbf{v}\times \mathbf{B}).}$

Applicability of ideal MHD to plasmas

Ideal MHD is only strictly applicable when:

1. The plasma is strongly collisional, so that the time scale of collisions is shorter than the other characteristic times in the system, and the particle distributions are therefore close to Maxwellian.
2. The resistivity due to these collisions is small. In particular, the typical magnetic diffusion times over any scale length present in the system must be longer than any time scale of interest.
3. Interest in length scales much longer than the ion skin depth and Larmor radius perpendicular to the field, long enough along the field to ignore Landau damping, and time scales much longer than the ion gyration time (system is smooth and slowly evolving).

Importance of resistivity

In an imperfectly conducting fluid the magnetic field can generally move through the fluid following a diffusion law with the resistivity of the plasma serving as a diffusion constant. This means that solutions to the ideal MHD equations are only applicable for a limited time for a region of a given size before diffusion becomes too important to ignore. One can estimate the diffusion time across a solar active region (from collisional resistivity) to be hundreds to thousands of years, much longer than the actual lifetime of a sunspot—so it would seem reasonable to ignore the resistivity. By contrast, a meter-sized volume of seawater has a magnetic diffusion time measured in milliseconds.

Even in physical systems—which are large and conductive enough that simple estimates of the Lundquist number suggest that the resistivity can be ignored—resistivity may still be important: many instabilities exist that can increase the effective resistivity of the plasma by factors of more than 10⁹. The enhanced resistivity is usually the result of the formation of small scale structure like current sheets or fine scale magnetic turbulence, introducing small spatial scales into the system over which ideal MHD is broken and magnetic diffusion can occur quickly. When this happens, magnetic reconnection may occur in the plasma to release stored magnetic energy as waves, bulk mechanical acceleration of material, particle acceleration, and heat.

Magnetic reconnection in highly conductive systems is important because it concentrates energy in time and space, so that gentle forces applied to a plasma for long periods of time can cause violent explosions and bursts of radiation.

When the fluid cannot be considered as completely conductive, but the other conditions for ideal MHD are satisfied, it is possible to use an extended model called resistive MHD. This includes an extra term in Ohm's Law which models the collisional resistivity. Generally MHD computer simulations are at least somewhat resistive because their computational grid introduces a numerical resistivity.

Structures in MHD systems

Further information: Magnetosphere particle motion

Schematic view of the different current systems which shape the Earth's magnetosphere

In many MHD systems most of the electric current is compressed into thin nearly-two-dimensional ribbons termed current sheets. These can divide the fluid into magnetic domains, inside of which the currents are relatively weak. Current sheets in the solar corona are thought to be between a few meters and a few kilometers in thickness, which is quite thin compared to the magnetic domains (which are thousands to hundreds of thousands of kilometers across). Another example is in the Earth's magnetosphere, where current sheets separate topologically distinct domains, isolating most of the Earth's ionosphere from the solar wind.

Waves

See also: Waves in plasmas

The wave modes derived using the MHD equations are called magnetohydrodynamic waves or MHD waves. There are three MHD wave modes that can be derived from the linearized ideal-MHD equations for a fluid with a uniform and constant magnetic field:

• Alfvén waves
• Slow magnetosonic waves
• Fast magnetosonic waves

Phase velocity plotted with respect to θ

v_A > v_s

 

v_A < v_s

These modes have phase velocities that are independent of the magnitude of the wavevector, so they experience no dispersion. The phase velocity depends on the angle between the wave vector k and the magnetic field B. An MHD wave propagating at an arbitrary angle θ with respect to the time independent or bulk field B₀ will satisfy the dispersion relation

${\displaystyle \frac{\omega }{k}=v_A\cos \theta }$

where

${\displaystyle v_A=\frac{B_0}{\sqrt{{\mu }_0\rho }}}$

is the Alfvén speed. This branch corresponds to the shear Alfvén mode. Additionally the dispersion equation gives

${\displaystyle \frac{\omega }{k}={\left(\frac{1}{2}\left(v_A^2+v_s^2\right)\pm \frac{1}{2}\sqrt{{\left(v_A^2+v_s^2\right)}^2-4v_s^2{v}_A^2{\cos }^2\theta }\right)}^{\frac{1}{2}}}$

where

${\displaystyle v_s=\sqrt{\frac{\gamma p}{\rho }}}$

is the ideal gas speed of sound. The plus branch corresponds to the fast-MHD wave mode and the minus branch corresponds to the slow-MHD wave mode. A summary of the properties of these waves is provided:

Mode	Type	Limiting phase speeds		Group velocity	Direction of energy flow
		${\displaystyle \mathbf{k}\parallel \mathbf{B}}$	${\displaystyle \mathbf{k}\perp \mathbf{B}}$
Alfvén wave	transversal; incompressible	$v_A$	${\displaystyle 0}$	${\displaystyle \frac{\mathbf{B}}{\sqrt{{\mu }_0\rho }}}$	${\displaystyle \mathbf{Q}\parallel \mathbf{B}}$
Fast magnetosonic wave	neither transversal nor longitudinal; compressional	${\displaystyle max(v_A,v_s)}$	${\displaystyle \sqrt{v_A^2+v_s^2}}$	equal to phase velocity	approx. ${\displaystyle \mathbf{Q}\parallel \mathbf{k}}$
Slow magnetosonic wave		${\displaystyle min(v_A,v_s)}$	${\displaystyle 0}$		approx. ${\displaystyle \mathbf{Q}\parallel \mathbf{B}}$

The MHD oscillations will be damped if the fluid is not perfectly conducting but has a finite conductivity, or if viscous effects are present.

MHD waves and oscillations are a popular tool for the remote diagnostics of laboratory and astrophysical plasmas, for example, the corona of the Sun (Coronal seismology).

Extensions

Resistive

Resistive MHD describes magnetized fluids with finite electron diffusivity (η ≠ 0). This diffusivity leads to a breaking in the magnetic topology; magnetic field lines can 'reconnect' when they collide. Usually this term is small and reconnections can be handled by thinking of them as not dissimilar to shocks; this process has been shown to be important in the Earth-Solar magnetic interactions.

Extended

Extended MHD describes a class of phenomena in plasmas that are higher order than resistive MHD, but which can adequately be treated with a single fluid description. These include the effects of Hall physics, electron pressure gradients, finite Larmor Radii in the particle gyromotion, and electron inertia.

Two-fluid

Two-fluid MHD describes plasmas that include a non-negligible Hall electric field. As a result, the electron and ion momenta must be treated separately. This description is more closely tied to Maxwell's equations as an evolution equation for the electric field exists.

Hall

In 1960, M. J. Lighthill criticized the applicability of ideal or resistive MHD theory for plasmas. It concerned the neglect of the "Hall current term" in Ohm's law, a frequent simplification made in magnetic fusion theory. Hall-magnetohydrodynamics (HMHD) takes into account this electric field description of magnetohydrodynamics, and Ohm's law takes the form

${\displaystyle \mathbf{E}+\mathbf{v}\times \mathbf{B}\underset{\text{Hall current term}}{\underbrace{-\frac{1}{n_{e}e}(\mathbf{J}\times \mathbf{B})}}=\eta \mathbf{J},}$

where $n_e$ is the electron number density and $e$ is the elementary charge. The most important difference is that in the absence of field line breaking, the magnetic field is tied to the electrons and not to the bulk fluid.

Electron MHD

Electron Magnetohydrodynamics (EMHD) describes small scales plasmas when electron motion is much faster than the ion one. The main effects are changes in conservation laws, additional resistivity, importance of electron inertia. Many effects of Electron MHD are similar to effects of the Two fluid MHD and the Hall MHD. EMHD is especially important for z-pinch, magnetic reconnection, ion thrusters, neutron stars, and plasma switches.

Collisionless

MHD is also often used for collisionless plasmas. In that case the MHD equations are derived from the Vlasov equation.

Reduced

By using a multiscale analysis the (resistive) MHD equations can be reduced to a set of four closed scalar equations. This allows for, amongst other things, more efficient numerical calculations.

Limitations

Importance of kinetic effects

Another limitation of MHD (and fluid theories in general) is that they depend on the assumption that the plasma is strongly collisional (this is the first criterion listed above), so that the time scale of collisions is shorter than the other characteristic times in the system, and the particle distributions are Maxwellian. This is usually not the case in fusion, space and astrophysical plasmas. When this is not the case, or the interest is in smaller spatial scales, it may be necessary to use a kinetic model which properly accounts for the non-Maxwellian shape of the distribution function. However, because MHD is relatively simple and captures many of the important properties of plasma dynamics it is often qualitatively accurate and is therefore often the first model tried.

Effects which are essentially kinetic and not captured by fluid models include double layers, Landau damping, a wide range of instabilities, chemical separation in space plasmas and electron runaway. In the case of ultra-high intensity laser interactions, the incredibly short timescales of energy deposition mean that hydrodynamic codes fail to capture the essential physics.

Applications

Geophysics

Beneath the Earth's mantle lies the core, which is made up of two parts: the solid inner core and liquid outer core. Both have significant quantities of iron. The liquid outer core moves in the presence of the magnetic field and eddies are set up into the same due to the Coriolis effect. These eddies develop a magnetic field which boosts Earth's original magnetic field—a process which is self-sustaining and is called the geomagnetic dynamo.

Reversals of Earth's magnetic field

Based on the MHD equations, Glatzmaier and Paul Roberts have made a supercomputer model of the Earth's interior. After running the simulations for thousands of years in virtual time, the changes in Earth's magnetic field can be studied. The simulation results are in good agreement with the observations as the simulations have correctly predicted that the Earth's magnetic field flips every few hundred thousand years. During the flips, the magnetic field does not vanish altogether—it just gets more complex.

Earthquakes

Some monitoring stations have reported that earthquakes are sometimes preceded by a spike in ultra low frequency (ULF) activity. A remarkable example of this occurred before the 1989 Loma Prieta earthquake in California, although a subsequent study indicates that this was little more than a sensor malfunction. On December 9, 2010, geoscientists announced that the DEMETER satellite observed a dramatic increase in ULF radio waves over Haiti in the month before the magnitude 7.0 M_w 2010 earthquake. Researchers are attempting to learn more about this correlation to find out whether this method can be used as part of an early warning system for earthquakes.

Space Physics

The study of space plasmas near Earth and throughout the Solar System is known as space physics. Areas researched within space physics encompass a large number of topics, ranging from the ionosphere to auroras, Earth's magnetosphere, the Solar wind, and coronal mass ejections.

MHD forms the framework for understanding how populations of plasma interact within the local geospace environment. Researchers have developed global models using MHD to simulate phenomena within Earth's magnetosphere, such as the location of Earth's magnetopause (the boundary between the Earth's magnetic field and the solar wind), the formation of the ring current, auroral electrojets, and geomagnetically induced currents.

One prominent use of global MHD models is in space weather forecasting. Intense solar storms have the potential to cause extensive damage to satellites and infrastructure, thus it is crucial that such events are detected early. The Space Weather Prediction Center (SWPC) runs MHD models to predict the arrival and impacts of space weather events at Earth.

Astrophysics

MHD applies to astrophysics, including stars, the interplanetary medium (space between the planets), and possibly within the interstellar medium (space between the stars) and jets. Most astrophysical systems are not in local thermal equilibrium, and therefore require an additional kinematic treatment to describe all the phenomena within the system (see Astrophysical plasma).

Sunspots are caused by the Sun's magnetic fields, as Joseph Larmor theorized in 1919. The solar wind is also governed by MHD. The differential solar rotation may be the long-term effect of magnetic drag at the poles of the Sun, an MHD phenomenon due to the Parker spiral shape assumed by the extended magnetic field of the Sun.

Previously, theories describing the formation of the Sun and planets could not explain how the Sun has 99.87% of the mass, yet only 0.54% of the angular momentum in the Solar System. In a closed system such as the cloud of gas and dust from which the Sun was formed, mass and angular momentum are both conserved. That conservation would imply that as the mass concentrated in the center of the cloud to form the Sun, it would spin faster, much like a skater pulling their arms in. The high speed of rotation predicted by early theories would have flung the proto-Sun apart before it could have formed. However, magnetohydrodynamic effects transfer the Sun's angular momentum into the outer solar system, slowing its rotation.

Breakdown of ideal MHD (in the form of magnetic reconnection) is known to be the likely cause of solar flares. The magnetic field in a solar active region over a sunspot can store energy that is released suddenly as a burst of motion, X-rays, and radiation when the main current sheet collapses, reconnecting the field.

Sensors

Magnetohydrodynamic sensors are used for precision measurements of angular velocities in inertial navigation systems such as in aerospace engineering. Accuracy improves with the size of the sensor. The sensor is capable of surviving in harsh environments.

Engineering

MHD is related to engineering problems such as plasma confinement, liquid-metal cooling of nuclear reactors, and electromagnetic casting (among others).

A magnetohydrodynamic drive or MHD propulsor is a method for propelling seagoing vessels using only electric and magnetic fields with no moving parts, using magnetohydrodynamics. The working principle involves electrification of the propellant (gas or water) which can then be directed by a magnetic field, pushing the vehicle in the opposite direction. Although some working prototypes exist, MHD drives remain impractical.

The first prototype of this kind of propulsion was built and tested in 1965 by Steward Way, a professor of mechanical engineering at the University of California, Santa Barbara. Way, on leave from his job at Westinghouse Electric, assigned his senior-year undergraduate students to develop a submarine with this new propulsion system. In the early 1990s, a foundation in Japan (Ship & Ocean Foundation (Minato-ku, Tokyo)) built an experimental boat, the Yamato-1, which used a magnetohydrodynamic drive incorporating a superconductor cooled by liquid helium, and could travel at 15 km/h.

MHD power generation fueled by potassium-seeded coal combustion gas showed potential for more efficient energy conversion (the absence of solid moving parts allows operation at higher temperatures), but failed due to cost-prohibitive technical difficulties. One major engineering problem was the failure of the wall of the primary-coal combustion chamber due to abrasion.

In microfluidics, MHD is studied as a fluid pump for producing a continuous, nonpulsating flow in a complex microchannel design.

MHD can be implemented in the continuous casting process of metals to suppress instabilities and control the flow.

Industrial MHD problems can be modeled using the open-source software EOF-Library. Two simulation examples are 3D MHD with a free surface for electromagnetic levitation melting, and liquid metal stirring by rotating permanent magnets.

Magnetic drug targeting

An important task in cancer research is developing more precise methods for delivery of medicine to affected areas. One method involves the binding of medicine to biologically compatible magnetic particles (such as ferrofluids), which are guided to the target via careful placement of permanent magnets on the external body. Magnetohydrodynamic equations and finite element analysis are used to study the interaction between the magnetic fluid particles in the bloodstream and the external magnetic field.

Interpreter (computing)

From Wikipedia, the free encyclopedia

W3sDesign Interpreter Design Pattern UML

In computer science, an interpreter is a computer program that directly executes instructions written in a programming or scripting language, without requiring them previously to have been compiled into a machine language program. An interpreter generally uses one of the following strategies for program execution:

1. Parse the source code and perform its behavior directly;
2. Translate source code into some efficient intermediate representation or object code and immediately execute that;
3. Explicitly execute stored precompiled bytecode made by a compiler and matched with the interpreter Virtual Machine.

Early versions of Lisp programming language and minicomputer and microcomputer BASIC dialects would be examples of the first type. Perl, Raku, Python, MATLAB, and Ruby are examples of the second, while UCSD Pascal is an example of the third type. Source programs are compiled ahead of time and stored as machine independent code, which is then linked at run-time and executed by an interpreter and/or compiler (for JIT systems). Some systems, such as Smalltalk and contemporary versions of BASIC and Java may also combine two and three. Interpreters of various types have also been constructed for many languages traditionally associated with compilation, such as Algol, Fortran, Cobol, C and C++.

While interpretation and compilation are the two main means by which programming languages are implemented, they are not mutually exclusive, as most interpreting systems also perform some translation work, just like compilers. The terms "interpreted language" or "compiled language" signify that the canonical implementation of that language is an interpreter or a compiler, respectively. A high-level language is ideally an abstraction independent of particular implementations.

History

Interpreters were used as early as 1952 to ease programming within the limitations of computers at the time (e.g. a shortage of program storage space, or no native support for floating point numbers). Interpreters were also used to translate between low-level machine languages, allowing code to be written for machines that were still under construction and tested on computers that already existed. The first interpreted high-level language was Lisp. Lisp was first implemented by Steve Russell on an IBM 704 computer. Russell had read John McCarthy's paper, "Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I", and realized (to McCarthy's surprise) that the Lisp eval function could be implemented in machine code.^[4] The result was a working Lisp interpreter which could be used to run Lisp programs, or more properly, "evaluate Lisp expressions".

General operation

An interpreter usually consists of a set of known commands it can execute, and a list of these commands in the order a programmer wishes to execute them. Each command (also known as an Instruction) contains the data the programmer wants to mutate, and information on how to mutate the data. For example, an interpreter might read ADD Books, 5 and interpret it as a request to add five to the Books variable.

Interpreters have a wide variety of instructions which are specialized to perform different tasks, but you will commonly find interpreter instructions for basic mathematical operations, branching, and memory management, making most interpreters Turing complete. Many interpreters are also closely integrated with a garbage collector and debugger.

Compilers versus interpreters

An illustration of the linking process. Object files and static libraries are assembled into a new library or executable

Programs written in a high-level language are either directly executed by some kind of interpreter or converted into machine code by a compiler (and assembler and linker) for the CPU to execute.

While compilers (and assemblers) generally produce machine code directly executable by computer hardware, they can often (optionally) produce an intermediate form called object code. This is basically the same machine specific code but augmented with a symbol table with names and tags to make executable blocks (or modules) identifiable and relocatable. Compiled programs will typically use building blocks (functions) kept in a library of such object code modules. A linker is used to combine (pre-made) library files with the object file(s) of the application to form a single executable file. The object files that are used to generate an executable file are thus often produced at different times, and sometimes even by different languages (capable of generating the same object format).

A simple interpreter written in a low-level language (e.g. assembly) may have similar machine code blocks implementing functions of the high-level language stored, and executed when a function's entry in a look up table points to that code. However, an interpreter written in a high-level language typically uses another approach, such as generating and then walking a parse tree, or by generating and executing intermediate software-defined instructions, or both.

Thus, both compilers and interpreters generally turn source code (text files) into tokens, both may (or may not) generate a parse tree, and both may generate immediate instructions (for a stack machine, quadruple code, or by other means). The basic difference is that a compiler system, including a (built in or separate) linker, generates a stand-alone machine code program, while an interpreter system instead performs the actions described by the high-level program.

A compiler can thus make almost all the conversions from source code semantics to the machine level once and for all (i.e. until the program has to be changed) while an interpreter has to do some of this conversion work every time a statement or function is executed. However, in an efficient interpreter, much of the translation work (including analysis of types, and similar) is factored out and done only the first time a program, module, function, or even statement, is run, thus quite akin to how a compiler works. However, a compiled program still runs much faster, under most circumstances, in part because compilers are designed to optimize code, and may be given ample time for this. This is especially true for simpler high-level languages without (many) dynamic data structures, checks, or type checking.

In traditional compilation, the executable output of the linkers (.exe files or .dll files or a library, see picture) is typically relocatable when run under a general operating system, much like the object code modules are but with the difference that this relocation is done dynamically at run time, i.e. when the program is loaded for execution. On the other hand, compiled and linked programs for small embedded systems are typically statically allocated, often hard coded in a NOR flash memory, as there is often no secondary storage and no operating system in this sense.

Historically, most interpreter systems have had a self-contained editor built in. This is becoming more common also for compilers (then often called an IDE), although some programmers prefer to use an editor of their choice and run the compiler, linker and other tools manually. Historically, compilers predate interpreters because hardware at that time could not support both the interpreter and interpreted code and the typical batch environment of the time limited the advantages of interpretation.

Development cycle

During the software development cycle, programmers make frequent changes to source code. When using a compiler, each time a change is made to the source code, they must wait for the compiler to translate the altered source files and link all of the binary code files together before the program can be executed. The larger the program, the longer the wait. By contrast, a programmer using an interpreter does a lot less waiting, as the interpreter usually just needs to translate the code being worked on to an intermediate representation (or not translate it at all), thus requiring much less time before the changes can be tested. Effects are evident upon saving the source code and reloading the program. Compiled code is generally less readily debugged as editing, compiling, and linking are sequential processes that have to be conducted in the proper sequence with a proper set of commands. For this reason, many compilers also have an executive aid, known as a Makefile and program. The Makefile lists compiler and linker command lines and program source code files, but might take a simple command line menu input (e.g. "Make 3") which selects the third group (set) of instructions then issues the commands to the compiler, and linker feeding the specified source code files.

Distribution

A compiler converts source code into binary instruction for a specific processor's architecture, thus making it less portable. This conversion is made just once, on the developer's environment, and after that the same binary can be distributed to the user's machines where it can be executed without further translation. A cross compiler can generate binary code for the user machine even if it has a different processor than the machine where the code is compiled.

An interpreted program can be distributed as source code. It needs to be translated in each final machine, which takes more time but makes the program distribution independent of the machine's architecture. However, the portability of interpreted source code is dependent on the target machine actually having a suitable interpreter. If the interpreter needs to be supplied along with the source, the overall installation process is more complex than delivery of a monolithic executable since the interpreter itself is part of what need to be installed.

The fact that interpreted code can easily be read and copied by humans can be of concern from the point of view of copyright. However, various systems of encryption and obfuscation exist. Delivery of intermediate code, such as bytecode, has a similar effect to obfuscation, but bytecode could be decoded with a decompiler or disassembler.

Efficiency

The main disadvantage of interpreters is that an interpreted program typically runs slower than if it had been compiled. The difference in speeds could be tiny or great; often an order of magnitude and sometimes more. It generally takes longer to run a program under an interpreter than to run the compiled code but it can take less time to interpret it than the total time required to compile and run it. This is especially important when prototyping and testing code when an edit-interpret-debug cycle can often be much shorter than an edit-compile-run-debug cycle.

Interpreting code is slower than running the compiled code because the interpreter must analyze each statement in the program each time it is executed and then perform the desired action, whereas the compiled code just performs the action within a fixed context determined by the compilation. This run-time analysis is known as "interpretive overhead". Access to variables is also slower in an interpreter because the mapping of identifiers to storage locations must be done repeatedly at run-time rather than at compile time.

There are various compromises between the development speed when using an interpreter and the execution speed when using a compiler. Some systems (such as some Lisps) allow interpreted and compiled code to call each other and to share variables. This means that once a routine has been tested and debugged under the interpreter it can be compiled and thus benefit from faster execution while other routines are being developed. Many interpreters do not execute the source code as it stands but convert it into some more compact internal form. Many BASIC interpreters replace keywords with single byte tokens which can be used to find the instruction in a jump table. A few interpreters, such as the PBASIC interpreter, achieve even higher levels of program compaction by using a bit-oriented rather than a byte-oriented program memory structure, where commands tokens occupy perhaps 5 bits, nominally "16-bit" constants are stored in a variable-length code requiring 3, 6, 10, or 18 bits, and address operands include a "bit offset". Many BASIC interpreters can store and read back their own tokenized internal representation.

Regression

Interpretation cannot be used as the sole method of execution: even though an interpreter can itself be interpreted and so on, a directly executed program is needed somewhere at the bottom of the stack because the code being interpreted is not, by definition, the same as the machine code that the CPU can execute.

Variations

Bytecode interpreters

Main article: Bytecode

There is a spectrum of possibilities between interpreting and compiling, depending on the amount of analysis performed before the program is executed. For example, Emacs Lisp is compiled to bytecode, which is a highly compressed and optimized representation of the Lisp source, but is not machine code (and therefore not tied to any particular hardware). This "compiled" code is then interpreted by a bytecode interpreter (itself written in C). The compiled code in this case is machine code for a virtual machine, which is implemented not in hardware, but in the bytecode interpreter. Such compiling interpreters are sometimes also called compreters. In a bytecode interpreter each instruction starts with a byte, and therefore bytecode interpreters have up to 256 instructions, although not all may be used. Some bytecodes may take multiple bytes, and may be arbitrarily complicated.

Control tables - that do not necessarily ever need to pass through a compiling phase - dictate appropriate algorithmic control flow via customized interpreters in similar fashion to bytecode interpreters.

Threaded code interpreters

Main article: Threaded code

Threaded code interpreters are similar to bytecode interpreters but instead of bytes they use pointers. Each "instruction" is a word that points to a function or an instruction sequence, possibly followed by a parameter. The threaded code interpreter either loops fetching instructions and calling the functions they point to, or fetches the first instruction and jumps to it, and every instruction sequence ends with a fetch and jump to the next instruction. Unlike bytecode there is no effective limit on the number of different instructions other than available memory and address space. The classic example of threaded code is the Forth code used in Open Firmware systems: the source language is compiled into "F code" (a bytecode), which is then interpreted by a virtual machine.

Abstract syntax tree interpreters

Main article: Abstract syntax tree

In the spectrum between interpreting and compiling, another approach is to transform the source code into an optimized abstract syntax tree (AST), then execute the program following this tree structure, or use it to generate native code just-in-time. In this approach, each sentence needs to be parsed just once. As an advantage over bytecode, the AST keeps the global program structure and relations between statements (which is lost in a bytecode representation), and when compressed provides a more compact representation. Thus, using AST has been proposed as a better intermediate format for just-in-time compilers than bytecode. Also, it allows the system to perform better analysis during runtime.

However, for interpreters, an AST causes more overhead than a bytecode interpreter, because of nodes related to syntax performing no useful work, of a less sequential representation (requiring traversal of more pointers) and of overhead visiting the tree.

Just-in-time compilation

Main article: Just-in-time compilation

Further blurring the distinction between interpreters, bytecode interpreters and compilation is just-in-time (JIT) compilation, a technique in which the intermediate representation is compiled to native machine code at runtime. This confers the efficiency of running native code, at the cost of startup time and increased memory use when the bytecode or AST is first compiled. The earliest published JIT compiler is generally attributed to work on LISP by John McCarthy in 1960. Adaptive optimization is a complementary technique in which the interpreter profiles the running program and compiles its most frequently executed parts into native code. The latter technique is a few decades old, appearing in languages such as Smalltalk in the 1980s.

Just-in-time compilation has gained mainstream attention amongst language implementers in recent years, with Java, the .NET Framework, most modern JavaScript implementations, and Matlab now including JIT compilers.

Template Interpreter

Making the distinction between compilers and interpreters yet again even more vague is a special interpreter design known as a template interpreter. Rather than implement the execution of code by virtue of a large switch statement containing every possible bytecode, while operating on a software stack or a tree walk, a template interpreter maintains a large array of bytecode (or any efficient intermediate representation) mapped directly to corresponding native machine instructions that can be executed on the host hardware as key value pairs (or in more efficient designs, direct addresses to the native instructions), known as a "Template". When the particular code segment is executed the interpreter simply loads or jumps to the opcode mapping in the template and directly runs it on the hardware. Due to its design, the template interpreter very strongly resembles a just-in-time compiler rather than a traditional interpreter, however it is technically not a JIT due to the fact that it merely translates code from the language into native calls one opcode at a time rather than creating optimized sequences of CPU executable instructions from the entire code segment. Due to the interpreter's simple design of simply passing calls directly to the hardware rather than implementing them directly, it is much faster than every other type, even bytecode interpreters, and to an extent less prone to bugs, but as a tradeoff is more difficult to maintain due to the interpreter having to support translation to multiple different architectures instead of a platform independent virtual machine/stack. To date, the only template interpreter implementations of widely known languages to exist are the interpreter within Java's official reference implementation, the Sun HotSpot Java Virtual Machine, and the Ignition Interpreter in the Google V8 javascript execution engine.

Self-interpreter

Main article: Meta-circular evaluator

A self-interpreter is a programming language interpreter written in a programming language which can interpret itself; an example is a BASIC interpreter written in BASIC. Self-interpreters are related to self-hosting compilers.

If no compiler exists for the language to be interpreted, creating a self-interpreter requires the implementation of the language in a host language (which may be another programming language or assembler). By having a first interpreter such as this, the system is bootstrapped and new versions of the interpreter can be developed in the language itself. It was in this way that Donald Knuth developed the TANGLE interpreter for the language WEB of the industrial standard TeX typesetting system.

Defining a computer language is usually done in relation to an abstract machine (so-called operational semantics) or as a mathematical function (denotational semantics). A language may also be defined by an interpreter in which the semantics of the host language is given. The definition of a language by a self-interpreter is not well-founded (it cannot define a language), but a self-interpreter tells a reader about the expressiveness and elegance of a language. It also enables the interpreter to interpret its source code, the first step towards reflective interpreting.

An important design dimension in the implementation of a self-interpreter is whether a feature of the interpreted language is implemented with the same feature in the interpreter's host language. An example is whether a closure in a Lisp-like language is implemented using closures in the interpreter language or implemented "manually" with a data structure explicitly storing the environment. The more features implemented by the same feature in the host language, the less control the programmer of the interpreter has; a different behavior for dealing with number overflows cannot be realized if the arithmetic operations are delegated to corresponding operations in the host language.

Some languages such as Lisp and Prolog have elegant self-interpreters. Much research on self-interpreters (particularly reflective interpreters) has been conducted in the Scheme programming language, a dialect of Lisp. In general, however, any Turing-complete language allows writing of its own interpreter. Lisp is such a language, because Lisp programs are lists of symbols and other lists. XSLT is such a language, because XSLT programs are written in XML. A sub-domain of metaprogramming is the writing of domain-specific languages (DSLs).

Clive Gifford introduced a measure quality of self-interpreter (the eigenratio), the limit of the ratio between computer time spent running a stack of N self-interpreters and time spent to run a stack of N − 1 self-interpreters as N goes to infinity. This value does not depend on the program being run.

The book Structure and Interpretation of Computer Programs presents examples of meta-circular interpretation for Scheme and its dialects. Other examples of languages with a self-interpreter are Forth and Pascal.

Microcode

Main article: Microcode

Microcode is a very commonly used technique "that imposes an interpreter between the hardware and the architectural level of a computer". As such, the microcode is a layer of hardware-level instructions that implement higher-level machine code instructions or internal state machine sequencing in many digital processing elements. Microcode is used in general-purpose central processing units, as well as in more specialized processors such as microcontrollers, digital signal processors, channel controllers, disk controllers, network interface controllers, network processors, graphics processing units, and in other hardware.

Microcode typically resides in special high-speed memory and translates machine instructions, state machine data or other input into sequences of detailed circuit-level operations. It separates the machine instructions from the underlying electronics so that instructions can be designed and altered more freely. It also facilitates the building of complex multi-step instructions, while reducing the complexity of computer circuits. Writing microcode is often called microprogramming and the microcode in a particular processor implementation is sometimes called a microprogram.

More extensive microcoding allows small and simple microarchitectures to emulate more powerful architectures with wider word length, more execution units and so on, which is a relatively simple way to achieve software compatibility between different products in a processor family.

Computer processor

Even a non microcoding computer processor itself can be considered to be a parsing immediate execution interpreter that is written in a general purpose hardware description language such as VHDL to create a system that parses the machine code instructions and immediately executes them.

Applications

• Interpreters are frequently used to execute command languages, and glue languages since each operator executed in command language is usually an invocation of a complex routine such as an editor or compiler.
• Self-modifying code can easily be implemented in an interpreted language. This relates to the origins of interpretation in Lisp and artificial intelligence research.
• Virtualization. Machine code intended for a hardware architecture can be run using a virtual machine. This is often used when the intended architecture is unavailable, or among other uses, for running multiple copies.
• Sandboxing: While some types of sandboxes rely on operating system protections, an interpreter or virtual machine is often used. The actual hardware architecture and the originally intended hardware architecture may or may not be the same. This may seem pointless, except that sandboxes are not compelled to actually execute all the instructions the source code it is processing. In particular, it can refuse to execute code that violates any security constraints it is operating under.
• Emulators for running computer software written for obsolete and unavailable hardware on more modern equipment.