Shockley–Ramo theorem

The Shockley–Ramo theorem is a method for calculating the electric current induced by a charge moving in the vicinity of an electrode. Previously named simply the "Ramo Theorem", the modified name was introduced by D.S. McGregor et al. in 1998 <ref>McGregor, D.S.; He, Z.; Seifert, H.A.; Wehe, D.K.; Rojeski, R.A. (1998). "CdZnTe semiconductor parallel strip Frisch grid radiation detectors". IEEE Trans. Nuclear Sci. 45 (3): 443–449. Bibcode:1998ITNS...45..443M. doi:10.1109/23.682424.</ref> to recognize the contributions of both Shockley and Ramo to understanding the influence of mobile charges in a radiation detector. The theorem appeared in William Shockley's 1938 paper titled "Currents to Conductors Induced by a Moving Point Charge"<ref>Shockley, W. (1938). "Currents to Conductors Induced by a Moving Point Charge". Journal of Applied Physics. 9 (10): 635–636. Bibcode:1938JAP.....9..635S. doi:10.1063/1.1710367.</ref> and in Simon Ramo's 1939 paper titled "Currents Induced by Electron Motion".<ref>Ramo, S. (1939). "Currents Induced by Electron Motion". Proceedings of the IRE. 27 (9): 584–585. doi:10.1109/JRPROC.1939.228757. S2CID 51657875.</ref> It is based on the concept that the current induced in the electrode is due to the instantaneous change of electrostatic flux lines that end on the electrode, rather than the amount of charge received by the electrode per second (net charge flow rate).

The Shockley–Ramo theorem states that the instantaneous current <math>i</math> induced on a given electrode due to the motion of a charge is given by:

<math> i = E_v q v </math>

where

<math>q</math> is the charge of the particle;

<math>v</math> is its instantaneous velocity; and

<math>E_v</math> is the component of the electric field in the direction of <math>v</math> at the charge's instantaneous position, under the following conditions: charge removed, given electrode raised to unit potential, and all other conductors grounded.

The theorem has been applied to a wide variety of applications and fields, including semiconductor radiation detection,<ref>He, Z (2001). "Review of the Shockley–Ramo theorem and its application in semiconductor gamma-ray detectors" (PDF). Nuclear Instruments and Methods in Physics Research Section A. 463 (1–2): 250–267. Bibcode:2001NIMPA.463..250H. doi:10.1016/S0168-9002(01)00223-6.</ref> calculations of charge movement in proteins.<ref>Eisenberg, Bob; Nonner, Wolfgang (2007). "Shockley-Ramo theorem measures conformation changes of ion channels and proteins". Journal of Computational Electronics. 6 (1–3): 363–365. doi:10.1007/s10825-006-0130-6. S2CID 52236338.</ref>, or the detection of moving ions in vacuum for mass spectrometry<ref>Jarrold, Martin F. (2022-04-27). "Applications of Charge Detection Mass Spectrometry in Molecular Biology and Biotechnology". Chemical Reviews. 122 (8): 7415–7441. doi:10.1021/acs.chemrev.1c00377. ISSN 0009-2665. PMC 10842748. PMID 34637283. S2CID 238745706.</ref> or ion implantation.<ref>Räcke, Paul; Spemann, Daniel; Gerlach, Jürgen W.; Rauschenbach, Bernd; Meijer, Jan (2018-06-28). "Detection of small bunches of ions using image charges". Scientific Reports. 8 (1): 9781. Bibcode:2018NatSR...8.9781R. doi:10.1038/s41598-018-28167-6. ISSN 2045-2322. PMC 6023920. PMID 29955102.</ref>

External links

• J. H. Jeans, "Electricity and Magnetism," page 160, Cambridge, London, English (1927) – Green's Theorem as Simon Ramo used it to derive his theorem.
• Introduction to Radiation Detectors and Electronics – Lecture Notes by Helmuth Spieler which briefly discuss Ramo's Theorem.