Early History of Charged-Particle Traps

Appendix A Early History of Charged-Particle Traps Abstract Today, we see a broad variety of particle traps and related devices for confinement and study of charged particles in various fields of science and indus- try (Werth, Charged Particle Traps, Springer, Heidelberg; Werth, Charged Particle Traps II, Springer, Heidelberg; Ghosh, Ion Traps, Oxford University Press, Oxford; Stafford, Am Soc Mass Spectrom. 13(6):589). The multitude of realisations and applications of electromagnetic confinement cannot be easily overlooked as the vari- ability of particle confinement and the vast number of experimental techniques avail- able has allowed traps and related instrumentation to enter many different fields in physics and chemistry as well as in industrial processes and applied analysis, mainly in the form of mass spectrometry (Stafford, Am Soc Mass Spectrom. 13(6):589; March and Todd, Practical Aspects of Ion Trap Mass Spectometry, CRC Press, Boca Raton). Here, we would like to give a brief account of the main historical aspects of charged-particle confinement, of the principles, technical foundations and beginnings that led to the realisation of traps and to the 1989 Nobel Prize in Physics awarded to Hans Georg Dehmelt and Wolfgang Paul ‘for the invention of the ion trap technique’, at which point we choose to end our discussion. Mainly, we will look at the work of the people who pioneered the field and paved the way to the first working traps. These can be seen as belonging to two different families of traps, Penning traps and Paul traps, each of these families nowadays with numerous variations of the respective confinement concepts. Here, however, we just have a brief look at the developmental history of the trap concepts. A.1 Motion of Charges in Electric and Magnetic Fields Since traps for charged particles work on account of electric and magnetic fields, we briefly summarize the corresponding background before which the first steps towards particle confinement and traps have been made. By the end of the 19th century, the effects of electric and magnetic fields on the motion of charges had been expounded in a modern sense. James Clerk Maxwell’s © Springer International Publishing AG, part of Springer Nature 2018 347 M. Vogel, Particle Confinement in Penning Traps, Springer Series on Atomic, Optical, and Plasma Physics 100, https://doi.org/10.1007/978-3-319-76264-7 348 Appendix A: Early History of Charged-Particle Traps (1831–1879) [6] famous twenty equations, in their modern form of four partial differ- ential equations, appeared in ‘A Treatise on Electricity and Magnetism’ in 1873 [7] following a less compact presentation in ‘A Dynamical Theory of the Electromag- netic Field’ in 1865 [8]. Already before that, he had established a field-line picture in his four-article series ‘On physical lines of force’ in 1861 [9]. According to this picture, electric test charges follow electric fields lines that are created by charges or time-varying magnetic fields. In modern notation, this means we have a force FE acting on a test particle with electric charge q given by FE = qE, (A.1) when E is the vector describing the strength and direction of the electric field. The electric fields created by charges are given by Gauss’s law, published in 1813 by Carl Friedrich Gauss (1777–1885) [10], which became part of Maxwell’s equations (commonly the first one). The electric fields created by time-varying magnetic fields are given by Faraday’s law of induction, introduced by Michael Faraday (1791–1867) in 1831/32 [11, 12], which also became one of Maxwell’s laws, usually the third one. The motion of test charges in a magnetic field is governed by the Lorentz force, named after Hendrik Antoon Lorentz (1853–1928, Nobel Prize in 1902 together with Pieter Zeeman) [13]. It is a force perpendicular to the particle motion and to the magnetic field lines, such that in principle, a charged particle can perform a closed circular motion in a plane perpendicular to the axis of a homogeneous magnetic field, a cyclotron motion. The Lorentz force FB is given by FB = q(v × B), (A.2) when q again is the electric charge of the particle, v is its velocity and B is the magnetic field. The first derivation of the Lorentz force on a charged particle in a magnetic field is commonly attributed to Oliver Heaviside (1850–1925) in 1889 [14] although historians argue about an earlier origin in a paper by James Clerk Maxwell in 1865 [15]. In any case, Hendrik Lorentz derived it independently in 1895, a few years after Heaviside [16], and he became the namesake. A.2 Samuel Earnshaw and His Theorem Already before the work of Maxwell, British clergyman and mathematician Samuel Earnshaw (1805–1888) [17] in his text ‘On the nature of the molecular forces which regulate the constitution of the luminiferous ether’ [18] had proved a theorem from which it follows that it is not possible to create a static electromagnetic field that con- fines a test charge in all three dimensions. The proof argues with Laplace’s equation (after Pierre-Simon Laplace, 1749–1827), given by (Fig. A.1) ΔΦ =∇·E = 0, (A.3) Appendix A: Early History of Charged-Particle Traps 349 Fig. A.1 Part of Earnshaw’s 1842 statement from ‘On the nature of the molecular forces which regulate the constitution of the luminiferous ether’ [18] which states that the divergence ∇·E of the electric field in absence of charges is zero, and so is the second spatial derivative ΔΦ of the corresponding electric potential Φ. Confining a charge in all spatial dimensions (x, y, z) requires a restoring force for any dislocation from a central point in space, and hence requires the potential Φ to have a minimum there. For simplicity (and without loss of generality) looking at a linear restoring force, the corresponding potential has the harmonic form Φ ∝ (ax2 + by2 + cz2) (A.4) with real-valued positive coefficients a, b, c. Inserting this potential into Laplace’s equation directly leads to the relation a + b + c = 0, which has obviously no solution for positive a, b and c. This means that at least one coefficient must be negative, implying a repulsive force in this direction. Hence, the potential has the shape of a saddle, a two-dimensional surface with both positive and negative curvatures embedded in three-dimensional space. This destroys any dream of a trap for charged particles that uses a single static field for stable confinement. Obviously, there are two possible solutions: 1. Use more than one static field. This is the way to the Penning trap which employs a static electric field and a static magnetic field. 2. Use a static and a non-static field. This is the way to the Paul trap which employs a time-varying electric field that consists of a constant and a time-dependent component. The solution can also be more complicated than this, like for example in case of the combined trap which uses all of the above fields. Another way to approach the problem is not to go for stable confinement with a static equilibrium of charged particles in the trap potential, but to implement dynamical confinement which puts up requirements for the particle motion. One example of such a trap is the Kingdon trap. 350 Appendix A: Early History of Charged-Particle Traps A.3 Kenneth Hay Kingdon and Electric ‘Imprisonment’ One case of dynamical confinement is the nowadays so-called ‘Kingdon trap’, some- times ‘Kingdon cage’, named after Kenneth Hay Kingdon (1894–1982), who had studied at the University of Toronto and worked mainly on the topic of electric dis- charges for the General Electric company in Schenectady, New York [19]. In his 1923 publication ‘A Method for the Neutralization of Electron Space Charge by Positive Ionization at Very Low Gas Pressures’ he writes [20] ‘If a very small filament, diameter 0.01 cm, is run axially through a cylindrical anode with closed ends, positive ions formed between the electrodes can only rarely escape and will describe orbits around the filament until they lose sufficient energy by collision with gas molecules to enable them to fall into the cathode. The imprisoned ions, during their lives, neutralize a certain amount of the space charge between the electrodes.’ Kingdon does not use the word ‘trap’ in his publication, rather the first term used for some localisation of charged particles was ‘imprisonment’. He was not interested in the localisation of the ions, but to find an efficient way to counteract space charge created by the electrons in discharge devices. Hence, he did not study motional frequencies and trajectories in detail. As described by Kingdon, the device is a hollow cylinder (A in Fig. A.2) with a thin wire (C in Fig.A.2) along the central axis and a pair of flat caps (G in Fig.A.2) that close the cylinder. There are different voltages set to each of these three components (cylinder, wire and caps). The values of these voltages can be chosen such that particles with a finite angular momentum with respect to the central wire experience a restoring force in the radial plane, hence dynamically stabilising the radial motion. At the same time, the voltages set to the caps can act repulsive on the particles, such that they provide axial confinement. Overall, the particle trajectory is then limited to a certain part of the cylindrical device, however confinement is restricted to a certain range of dynamical parameters. Fig. A.2 Title and abstract from ‘A Method for the Neutralization of Electron Space Charge by Positive Ionization at Very Low Gas Pressures’ [20] from 1923 and the setup presented therein Appendix A: Early History of Charged-Particle Traps 351 The potential close to the central wire is logarithmic, but more complicated for larger orbits and closer to the caps.

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