Gaussian unit system

Readers may be aware that the equations and numerical values of a magnetic field change with the system used. It thus becomes necessary to review the basics of unit systems here. The units in magnetics have always been somewhat confusing. Both SI and Gaussian unit systems are widely used in the literature. This state of affairs may be understood in terms of the following ... 

In terms of the irrational susceptibility (ir), which is often used in connection with the older esu, emu, and Gaussian unit systems (see section 7.3 below), this equation becomes... 

One should avoid using non-SI units from the following unit systems the esu (electrostatic unit system), the emu (electromagnetic unit system) and the Gaussian unit system. However, equations relating these still widely used unit systems to the SI are listed in Chapter 7 of [1] which also makes extensive use of quantity calculus to help converting between those systems of units. 

The macroscopic Maxwell s equations in matter are (in the Gaussian unit system used throughout this handbook) ... 

The abbreviation au stands for atomic units , which is a system of units meant to simplify the equations of molecular and atomic quantum mechanics. The units of the au system are combinations of the fundamental units of mass (mass of the electron), charge (charge of the electron), and Planck s constant. By setting these three quantities equal to unity one gets simpler equations. The au system has a simple relation to the SI and Gaussian (cgs) systems of units. For example, 1 au of length = aQ (Bohr radius) = 5.29 x 10"9 cm =... 

In the present book, for magnetism we use the SI unit that is based on the MKS A (meter, kilogram, second, ampere) system. In accordance with that, the tesla (1T = 10" gauss) was presented as the magnetic unit in Chapter 17 (see Fig. 17.10a and b). It is useful to know both the SI and Gaussian systems and be able to convert between them. Thus, when one attempts to solve a magnetics problem, to avoid errors one is well advised to stick to a single convenient unit system. A useful conversion table of... 

A short digression on units is perhaps appropriate here. We shall use either Gaussian rrrrits in this book or, much more frequently, Hartree s atomic units. Gaussian units, as far as we are concerned, are identical with the old cgs system of units with the added proviso that charges are measured in unnamed electrostatic units, esu. The value of e is thus 4.803206808 X 10 esu. Keeping this number at hand is all that will be required to use Gaussian rmits in this book. 

So far we have employed gaussian units, which are more common in theoretical discussions. However, experimental results are generally discussed in terms of practical units. Since conversions between different systems of units can sometimes be confusing we include here an example. Consider R. In gaussian units E and are in statvolt/cm (for this is called gauss ), j in... 

In 1960, the eleventh General Conference on Weights and Measures recommended the International System of Units (Systeme International d Unites), abbreviated as SI units, for use in science SI units are essentially the rationalized mks system of units. Relations between SI units and Gaussian units are given in Table A.4 of the Appendix. Table A.5 allows one to convert equations from SI to Gaussian units. 

This algorithm, standard in the widely used GAUSSIAN program system, is a rank-m update of the Hessian matrix, in an orthonormal basis [356], A basis of unit vectors is constructed in the m -dimensional vector space spanned by the increments Aq. For k = 1, m, define... 

The two common unit systems employed for the description of nonlinear optical properties are the SI (or MKS) and Gaussian (or cgs) systems (Boyd24 mentions an alternative system of SI units that are not discussed further in this article, as it has not been used with organometallic complexes). In the Gaussian system, properties are described in units of esu. 

Still, units can be a nuisance. One difficulty is that much serious theoretical work is still done in centimeter-gram-second (cgs) or "Gaussian" units such is the case with the Level 3 derivations in this text. Most students learn applications in meter-kilogram-seconds (mks) "SI" or "Systeme International" units. Happily, practical formulae for... 

The first, permanent-dipole term is important only at zero frequency in the summation over imaginary sampling frequencies f . The relaxation time r is big enough that for f =i the permanent-dipole term in a is effectively zero this term counts only at zero frequency. In both mks (SI or Systeme International) and cgs ("Gaussian") units, the dipole moment //.dipole = qd for charges q separated by distance d. [See table S.8 and Eq. (L2.171) in Level 2.]... 

The system of units most frequently employed in nonlinear optics is the Gaussian (or cgs) system. Sporadically, the SI unit system is used. It is important to be able to convert between the two systems. However, not only do the units need to be con-... 

The above considerations leads to the somewhat troubling question of whether (128) represents the true non-relativistic limit of the Dirac equation in the presence of external fields. Referring back to (110) we have certainly obtained the non-relativistic limit of the free-particle part Lm, but we have in fact retained the interaction term as well as the Lagrangian of the free field. In order to obtain the proper non-relativistic limit, we must consider what is the non-relativistic limit of classical electrodynamics. This task is not facilitated by the fact that, contrary to purely mechanical systems, the laws of electrodynamics appear in different unit systems in which the speed of light appears differently. In the Gaussian system Maxwell s laws are given as... 

Gaussian units A system of units for electric and magnetic quantities based upon c.g.s. electrostatic and electromagnetic units. Although replaced by S1 units in most branches of science, they are, like Heavi-side-Lorentz units, still used in relativity theory and in particle physics. In Gaussian units, the electric and magnetic constants are both equal to unity. 

Unit conversion among magnetic properties depends on the dimensions used for the magnetic field, B. In the Gaussian and atomic units systems, electric fields and magnetic fields have the same dimensions, since the Lorentz force law is F (E -I- V X B/c). For these, Eq. [34] is valid for the conversion from atomic to Gaussian units. For S.I. units, where F = q(E -1- v x B), the conversion factor, F, is slightly different from Eq. [34] ... 

Two unit systems are commonly employed in describing NLO properties the SI (MKS) and the Gaussian (cgs) systems. One should note that many equations have a different form when written in these two systems of units, and that conversion between these two systems is frequently cumbersome. One should also be aware that definitions of hyperpolarizabilities and susceptibilities may differ between different authors because of the lack of general agreement whether the complex field amplitude in Eq. (2) should include a factor of 1/2 and whether the multiplying degeneracy factors [such as those in Eq. (3)] should be included in the hyperpolarizabilities. 

The electric and magnetic fields appearing in Sections 2.3.1 and 2.3.2 have been described in terms of the SI system of units. The Gaussian system of cgs units has frequently been employed in the theory of liquid crystals when magnetic fields are discussed. Gaussian units are considered by many to be natural units for the calculation and measurement of magnetic field effects in liquid crystals. Since much of the literature contains results in both Gaussian units and SI units, it seems appropriate at this point to make some comments on the conversion from one system of units to the other. A comprehensive account of the points touched upon here may be found in Jackson [132] or Moskowitz [206]. Readers should also be famihar with derived SI units. 

Unit systems related to electrical quantities can be confusing. Depending on the unit system, these equations can take different forms. The equations below are written for CGS (Gaussian) units as opposed to SI. 

Appendix D Unit Systems M 679 TABLE D.2 Conversion between CGS (Gaussian) units and SI units... 

---