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Radiation pressure

Force per area exerted by electromagnetic radiation; small for everyday light but important in astrophysics, laser physics, optical manipulation, and spacecraft propulsion.

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Overview

Radiation pressure is the mechanical pressure exerted on a surface by electromagnetic radiation. Photons carry momentum as well as energy, and when light or other electromagnetic waves strike matter they transfer some of that momentum. The resulting force per unit area can be observed in controlled experiments and plays a measurable role in many natural and technological settings. For a concise definition see radiation pressure.

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Advanced Composite Solar Sail System Artist’s Concept 5 (ACS3 SolarSailPush 001)
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How it arises and basic formula

In classical terms the flow of electromagnetic energy is described by the Poynting vector, and the momentum flux is related to that energy flux. A simple, widely used expression links intensity I (energy per unit area per unit time) to pressure p: for perfect absorption the pressure is p = I/c, where c is the speed of light; for perfect reflection the momentum change is doubled and p = 2I/c. Real materials produce intermediate values depending on reflectivity and scattering. For a compact summary of the energetics and momentum transfer see energy and momentum in light.

Historical measurements and demonstrations

The idea that electromagnetic radiation can exert pressure follows from electromagnetic theory developed in the 19th century. Direct laboratory measurements came later, when sensitive torsion balances and radiometers were used to detect the tiny forces involved. Some early devices, including the Crookes radiometer, are often discussed in this context; the radiometer's spinning vanes are driven primarily by thermal effects on residual gas molecules rather than by photon pressure itself. For accessible experimental descriptions consult experimental studies of light pressure.

Examples and applications

Although radiation pressure is negligible for most everyday forces, it becomes important where light intensities are large or over long distances. Notable examples include:

  • Solar sails: spacecraft that use sunlight momentum to produce continuous thrust without propellant.
  • Astrophysics: radiation pressure influences the structure of stellar atmospheres, drives stellar winds in massive stars, and helps shape comet tails by pushing dust away from the Sun.
  • Optical manipulation: focused laser beams can trap and move microscopic particles (optical tweezers) and contribute to laser cooling techniques.
  • Laboratory physics: precision experiments can use radiation pressure to measure properties of light and matter or to actuate micro- and nano-mechanical devices.

Radiation pressure should be distinguished from other radiative forces and effects. Scattering and absorption by particles involve momentum exchange but depend on size, composition, and angle. For charged particles, radiation can exert forces indirectly through induced currents or by Compton and Thomson scattering. In orbital dynamics, subtle effects such as the Poynting–Robertson drag arise when sunlight both exerts pressure and changes a particle's orbital energy. For further reading on related concepts see related radiation effects.

Practical note: the magnitude of radiation pressure at Earth from sunlight is small (on the order of micro- to milli-Newtons per square meter under ordinary conditions), but it accumulates over time or becomes significant in domains where conventional forces are absent or tiny, making it a useful and sometimes dominant influence in space and in precision optical systems.

History and proof

That light exerts a pressure was postulated by Johannes Kepler as an explanation for comet tails always directed away from the sun. James Clerk Maxwell derived in 1873 from Maxwell's equations within the framework of electrodynamics that electromagnetic waves can exert a pressure on bodies. He already showed that the radiation pressure of vertically incident electromagnetic waves is equal to the volumetric energy density wthe incident waves:

p_{{\mathrm {St}}}=w

In 1876, Adolfo Bartoli derived the existence of radiation pressure from thermodynamic considerations. He argued that by reflection of the light at a moving mirror, heat could be transferred from a cold to the hot body due to the Doppler effect. To avoid this violation of the second law of thermodynamics, it is necessary that the light exerts a pressure on the mirror. Therefore, the radiation pressure used to be called Maxwell-Bartolian pressure after its discoverers.

The first experimental confirmations came from Pyotr Nikolaevich Lebedev (1901) and from Ernest Fox Nichols and Gordon Ferrie Hull (1903). In 1972, the physicist Arthur Ashkin irradiated small plastic beads with laser light and was able to observe a change in motion under the microscope.

Statement

The electromagnetic radiation can be considered both as a stream of photons and as an electromagnetic wave. The radiation pressure can be derived from both models.

Particle model

A photon of frequency ν \nu transports the energy

E=h\cdot \nu (see photoelectric effect)

with the Planck quantum of action h. Due to the energy-momentum relation

{\displaystyle E={\sqrt {{\vec {p}}^{2}c^{2}+m^{2}c^{4}}}}

follows for the photon with a mass m=0a momentum {\vec {p}}with the magnitude:

{\displaystyle \left|{\vec {p}}\right|=h\cdot {\frac {\nu }{c}}}

The direction of the momentum is the direction of motion of the photon. The total momentum is conserved during absorption, emission and reflection, i.e. the interacting surface undergoes a momentum change in the corresponding direction. Multiple photons, i.e., a photon stream {\frac {{\mathrm d}N}{{\mathrm d}t}}with particle number N, when absorbed, cause a change in momentum per unit time, i.e., a force, of

{\frac {{\mathrm d}\left|{\vec p}\right|}{{\mathrm d}t}}={\frac {h\cdot \nu }{c}}\cdot {\frac {{\mathrm d}N}{{\mathrm d}t}}

If this force acts on a surface element at the angle of incidence\theta the surface normal. \mathrm {d} A, it generates the pressure p_{{{\mathrm {St}}}}of

p_{{{\mathrm {St}}}}=\cos \theta \cdot {\frac {{\mathrm d}\left|{\vec p}\right|}{{\mathrm d}t\cdot {\mathrm d}A}}={\frac {h\cdot \nu \cdot \cos \theta }{c}}\cdot {\frac {{\mathrm d}N}{{\mathrm d}t\cdot {\mathrm d}A}}={\frac {1}{c}}\cdot {\frac {{\mathrm d}\Phi _{e}}{{\mathrm d}A}}={\frac {E_{e}}{c}}

where \Phi _{e}is the radiation flux. A reflected photon takes a momentum of the same magnitude back with it, so in the case of reflection there is twice the momentum transfer to the interacting surface and thus twice the radiation pressure.

Wave model

The pressure exerted on a surface by a radiation field in vacuum can be (T_{{ij}})expressed by the Maxwell stress tensor For an absorbing surface with normal vector {\vec {n}}the radiation pressure is given by

p_{{\mathrm {St}}}\,n_{j}=\sum _{{i=1}}^{3}T_{{ij}}n_{i}

The components of the Maxwell voltage tensor can be calculated from the electric field strength {\vec {E}}and the magnetic flux density {\vec {B}}

{\displaystyle T_{ij}={\frac {1}{2}}\left(\varepsilon _{0}E^{2}+{\tfrac {1}{\mu _{0}}}B^{2}\right)\delta _{ij}-\varepsilon _{0}E_{i}E_{j}-{\tfrac {1}{\mu _{0}}}B_{i}B_{j}}

where δ \delta _{ij}the Kronecker delta, ε \varepsilon _{0}electric field constant, and μ \mu _{0}the magnetic field constant.

A more detailed explanation based on Maxwell's equations can be found, for example, in Jay Orear: Physics: Volume 2.

Momentum transfer upon reflection of the photon
Momentum transfer upon reflection of the photon

Application

The solar constant is approx. 1370 W/m². This results in a solar radiation pressure (SRP) at absorption of approx. 4.6 μPa. For perpendicular reflection it is twice as high. There have been ideas for some time to use this with solar sails as propulsion for interplanetary spacecraft.

More realistic is the generation of ion beams for medical applications, for example, by radiation pressure of short laser pulses on ultrathin foils. From a radiation intensity of about 1022 W/cm² in circular polarization, the radiation pressure outweighs the recoil effect known from inertial fusion and generates high-energy ions with narrower energy and angular distribution.

The function of the light mills, on the other hand, is not based on radiation pressure. This can be seen from the direction of rotation: the reflecting side of the blades is exposed to a higher radiation pressure than the blackened side, yet the mill rotates in exactly the opposite direction.

Astrophysics

In astrophysics, radiation pressure plays a significant role in explaining the dynamics of stars and interstellar clouds.

The tail of comets is caused to a substantial part by the radiation pressure, which "blows away" components of the coma. So the tail always points away from the sun, no matter in which direction the comet flies.

See also: Poynting-Robertson effect

Influence of radiation pressure and solar wind on comet Hale-Bopp.
Influence of radiation pressure and solar wind on comet Hale-Bopp.

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