Physics
Radiation Pressure
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. It is caused by the momentum transfer between the photons and the surface. This phenomenon is important in various fields of physics, including astrophysics, optics, and laser technology.
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5 Key excerpts on "Radiation Pressure"
- C.V. Heer(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
(2.30)} = ΑοΤ Ρ J Some common values of A are given in this table and a more ex-tensive list is given in the Handbook of Chemistry and Physics [2a]. Total emissivity and absorption are regarded as equivalent in this table. where (hv/c)k · ή is the momentum of the photon along the normal ή and k · ή = cos ψ is the area perpendicular to k. This can be related to the total energy density or intensity and upon integration yields P = -jp-(2.32b) This is the same relationship between energy density and pressure as that obtained in classical electromagnetic theory, in which the photon concept is not used. 50 RADIATION For some calculations, the flux of photons is of interest and for thermal radiation, the photons leaving a surface per second is Jnumber of thermal photons emitted per second byl [surface dS into dQ dv with polarization p J (2.33) The number of photons crossing a surface inside the cavity is given by Eq. (2.33) with A = 1. It is interesting to note that the pressure per photon is one-third of the photon energy and the pressure per particle in Chapter I was two-thirds of the kinetic energy of the particle. This is a direct con-sequence of the linear relationship between the energy and momentum of the photon, E = cp = fikc. Radiation Pressure is quite significant in astrophysical problems, but is quite difficult to observe in the laboratory. Heating caused by the radia-tion introduces thermal creep or radiometer pressures, which were discussed in Section 1.11.5, and are more than an order of magnitude greater than Radiation Pressure. The Radiation Pressure of a 1-W laser is appreciable [3] and can be used to accelerate small particles. In order to avoid the radiometric effect, the particles, of the order of 1 in diameter, were placed in a liquid.
eBook - PDFChaotic Dynamics In Hamiltonian Systems: With Applications To Celestial Mechanics
With Applications to Celestial Mechanics
- Harry Dankowicz(Author)
- 1997(Publication Date)
- World Scientific(Publisher)
The velocity-dependent term in this expression is known as the Poynting-Robertson drag, and the remaining term as Radiation Pressure. • The energy flux per unit area and unit time decays as r 2 , since F --L. (5.14) where r is the distance from the sun and L is the solar luminosity. It is therefore con-venient to express the Radiation Pressure as a fraction of the gravitational attraction 130 Application - Radiation Pressure I to the sun at distance r. In fact, the ratio between Radiation Pressure and gravitation is LAO r 2 L Q , Q , , where R and p are the radius and density, respectively, of the particle. The constant Q depends on the optical properties of the particle, as well as its size and the spectrum of the solar radiation. For particles larger than tens of microns, Q is essentially size- and constituent-independent and approximately equal to 1. For smaller particles, careful numerical integrations are necessary to obtain estimates of Q for different materials as a function of particle size. In the following sections we consider the effects of Radiation Pressure on particles of fractions-of-millimeter-size, and hence assume Q t**. Electromagnetic perturbations Solar radiation impacting on small particles can lead to permanent ionization, thus creating charged particles. In interplanetary space, these small particles experi-ence the effects of the heliosphere, the electromagnetic field associated with the sun. Similarly, planetary magnetic fields affect the dynamics of circumplanetary charged objects. For example, the earth's magnetic field results in high concentrations of electrons and ions in the so-called van Allen belts. Charged particles bounce back and forth between the magnetic poles while spiralling through the van Allen belts. Physical considerations 131 5.1.2 The bodies of the solar system In addition to the major planets and their moons, the solar system contains a plethora of smaller objects.
eBook - PDF- Donald L. Wise(Author)
- 1991(Publication Date)
- CRC Press(Publisher)
But the very fact that it does experience a force indicates that a certain pressure, and therefore a certain force, exists even after time averaging. This time-averaged nonzero pressure in a sound field is customarily called the Radiation Pressure and the force, the radiation force. If the sound waves were strictly harmonic and the medium linear, the radiation force would not exist. This then signifies that deviations from strict harmonicity of propa-gation and/or nonlinear response by the medium must be taken into account. The possible sources of such nonlinearities are the basic nonlinearity of the governing hydrodynamic equations themselves, the nonlinearity in the equation of state of the matter, and that due to finite amplitude waves which carry distortions in their propagating wavesforms. 1 The Radiation Pressure is usually small compared to the first-order, periodically varying sound pressure. For example, in a sound field in which the sound pressure is 1()3 dyn/cm 2 under normal conditions in air, the acoustic Radiation Pressure for normal incidence on a perfectly reflecting obstacle is of the order of 1 dynl cm 2 . 2 This is expressed by saying that the nonlinearity is of second order. It is customary to distinguish between Rayleigh and Langevin Radiation Pressure,3-6 depending on the physical situation and the boundary conditions involved. More specifically, the criterion is whether or not the motion of the sonicated fluid normal to the wave propagation is allowed. 7 If this lateral motion is not permitted and the mass of the irradiated fluid re:mains constant, one speaks of the Rayleigh Radiation Pressure. The Rayleigh case is thus typified by propagation in closed systems with no mass transfer with the thermodynamical universe. Interaction between the system, which is the sonicated fluid, and the universe then does not take place. On the other hand, if lateral motion is allowed, one speaks of Langevin Radiation Pressure.
- Dina Prialnik(Author)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
Thus as a crude approximation, the degeneracy pressure may be considered as insensitive to temperature. The approximation is good provided kT is only a fraction of the kinetic energy of a particle with the highest momentum p 0 ( n e ). A more accurate treatment of degeneracy pressure may be found in Appendix B . 3.4 The Radiation Pressure Radiation Pressure is due to photons that transfer momentum to gas particles whenever they are absorbed or scattered. In thermodynamic equilibrium the pho-ton distribution is isotropic and the number of photons with frequencies in the range ( ν, ν + dν ) is given by the Planck (blackbody distribution) function n ( ν ) dν = 8 πν 2 c 3 dν e hν kT − 1 . (3.39) The pressure is then readily obtained from Equation (3.4) : P rad = 1 3 ∞ 0 c hν c n ( ν ) dν = 1 3 aT 4 , (3.40) where a is the radiation constant a = 8 π 5 k 4 15 c 3 h 3 = 4 σ c . (3.41) Although the expression for Radiation Pressure was easily derived from the pressure integral, the concept deserves further (intuitive) explanation. Imagine a collimated beam of photons striking an atom. Each photon is absorbed, thereby exciting the atom, which consequently returns to its original state by emitting a photon. The direction of the emitted photon is random, the initial direction 3.5 The internal energy of gas and radiation 43 of the absorbed one having been ‘forgotten’. Each such interaction involves an exchange of momentum. By absorbing the photon, the atom gains momentum in the direction of the photon beam. When it emits a photon, the atom recoils in the direction opposite to that of the emitted photon. After a long series of such interactions, the random changes of momentum due to emission cancel out and the net change in the atom’s momentum is in the direction of the photon beam, as if material pressure has been exerted on it in that direction.
- F N H Robinson(Author)
- 1996(Publication Date)
- WSPC(Publisher)
CHAPTER 6 RELATIVISTIC DYNAMICS II 6.1 Radiation Pressure A-medium attenuated wave > Figure 6.1 Radiation Pressure In Figure 6.1 a plane electromagnetic wave of angular frequency © and characterised by fields E and H, falls at normal incidence from vacuum on the plane surface of a medium, whose only difference from vacuum is a small electric conductivity a « ©e 0 , so small that we can ignore any reflection, since this would be quadratic in a/coe 0 . In vacuum the wave propagates as e ± ^ t ' K o x) where K 0 =CO/C. In the medium K 0 is replaced (to first order in a) by K = K 0 -HioZ 0 , where 2 0 =(u 0 /s 0 )^ is the impedance of free space. Thus the amplitudes of the fields decay with distance as eT^ z o x . The electric field drives a current density J = aE and the electromagnetic force density will therefore be f a JxB = u 0 JxH = u. 0 aExH = u= 0 aE 0 xH 0 e-ff *o*. The total force per unit area acting on the medium is obtained by integrating this force per unit volume from x=0 to infinity, and this gives F = E 0 xH 0 /c. (6.D The rate at which momentum is brought up to unit area is thus 1/c times the rate E 0 x H 0 at which energy is brought up. The relation between the energy E and the momentum p of a plane electromagnetic wave is therefore E = pc. ( 6 -2 > This yields v = dE/dp = c, (6.3) 65 66 Relativity which need not surprise us, and the equation E 2 = p 2 c 2 . (6.4) This replaces E 2 = p 2 c 2 + m 0 2 c 4 , and corresponds to treating a photon as a particle of zero rest mass, i.e. jn o =0. However, if we write p = mv = mc, the inertial mass is still m=£/c 2 (as we assumed in Chapter 5). Thus in an inelastic collision in which energy is carried off by radiation the radiation will also carry off mass.
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