[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki43\/ion-trap-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki43\/ion-trap-wikipedia\/","headline":"Ion trap – Wikipedia","name":"Ion trap – Wikipedia","description":"before-content-x4 Device for trapping charged particles This article is about gas phase ions. For ions in cells, see ion trapping.","datePublished":"2014-01-23","dateModified":"2014-01-23","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki43\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki43\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/cc\/Ionenfalle_-_Quantencomputer.jpg\/300px-Ionenfalle_-_Quantencomputer.jpg","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/cc\/Ionenfalle_-_Quantencomputer.jpg\/300px-Ionenfalle_-_Quantencomputer.jpg","height":"225","width":"300"},"url":"https:\/\/wiki.edu.vn\/en\/wiki43\/ion-trap-wikipedia\/","wordCount":11757,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4Device for trapping charged particlesThis article is about gas phase ions. For ions in cells, see ion trapping.  Ion trap, shown here is one used for experiments towards realizing a quantum computer.An ion trap is a combination of electric and\/or magnetic fields used to capture charged particles \u2014 known as ions \u2014 often in a system isolated from an external environment. Atomic and molecular ion traps have a number of applications in physics and chemistry such as precision mass spectrometry, improved atomic frequency standards, and quantum computing.[1] In comparison to neutral atom traps, ion traps have deeper trapping potentials (up to several electronvolts) that do not depend on the internal electronic structure of a trapped ion. This makes ion traps more suitable for the study of light interactions with single atomic systems. The two most popular types of ion traps are the Penning trap, which forms a potential via a combination of static electric and magnetic fields, and the Paul trap which forms a potential via a combination of static and oscillating electric fields.[2]Penning traps can be used for precise magnetic measurements in spectroscopy. Studies of quantum state manipulation most often use the Paul trap. This may lead to a trapped ion quantum computer[3] and has already been used to create the world’s most accurate atomic clocks.[4][5]Electron guns (a device emitting high-speed electrons, used in CRTs) can use an ion trap to prevent degradation of the cathode by positive ions.A charged particle, such as an ion, feels a force from an electric field. As a consequence of Earnshaw’s theorem, it is not possible to confine an ion in an electrostatic field. However, physicists have various ways of working around this theorem by using combinations of static magnetic and electric fields (as in a Penning trap) or by oscillating electric fields (Paul trap). In the case of the latter, a common analysis begins by observing how an ion of charge e{displaystyle e} and mass M{displaystyle M} behaves in an a.c. electric field E=E0cos\u2061(\u03a9t){displaystyle mathbf {E} =mathbf {E} _{0}cos(Omega t)}. The force on the ion is given by F=eE{displaystyle mathbf {F} =emathbf {E} }, so by Newton’s second law we haveMr\u00a8=eE0cos\u2061(\u03a9t){displaystyle Mmathbf {ddot {r}} =emathbf {E} _{0}cos(Omega t)!} .Assuming that the ion has zero initial velocity, two successive integrations give the velocity and displacement asr\u02d9=eE0M\u03a9sin\u2061(\u03a9t){displaystyle mathbf {dot {r}} ={frac {emathbf {E} _{0}}{MOmega }}sin(Omega t)!} ,r=r0\u2212eE0M\u03a92cos\u2061(\u03a9t){displaystyle mathbf {r} =mathbf {r} _{0}-{frac {emathbf {E} _{0}}{MOmega ^{2}}}cos(Omega t)!} ,where r0{displaystyle mathbf {r} _{0}} is a constant of integration. Thus, the ion oscillates with angular frequency \u03a9{displaystyle Omega } and amplitude proportional to the electric field strength. A trapping potential can be realized by spatially varying the strength of the a.c. electric field.Table of ContentsLinear Paul Trap[edit]Penning Trap[edit]Ion trap mass spectrometers[edit]Penning ion trap[edit]Paul ion trap[edit]Kingdon trap and orbitrap[edit]Trapped ion quantum computer[edit]Cathode ray tubes[edit]See also[edit]References[edit]External links[edit]Linear Paul Trap[edit]The linear Paul trap uses an oscillating quadrupole field to trap ions radially and a static potential to confine ions axially. The quadrupole field is realized by four parallel electrodes laying in the z{displaystyle z}       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4-axis positioned at the corners of a square in the xy{displaystyle xy}-plane. Electrodes diagonally opposite each other are connected and an a.c. voltage V=V0cos\u2061(\u03a9t){displaystyle V=V_{0}cos(Omega t)} is applied. Along the z{displaystyle z}-axis, an analysis of the radial symmetry yields a potential[6]       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u03d5=\u03b1+\u03b2(x2\u2212y2){displaystyle phi =alpha +beta (x^{2}-y^{2})!} .The constants \u03b1{displaystyle alpha } and \u03b2{displaystyle beta } are determined by boundary conditions on the electrodes and        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u03d5{displaystyle phi } satisfies Laplace’s equation \u22072\u03d5=0{displaystyle nabla ^{2}phi =0}. Assuming the length of the electrodes r{displaystyle r} is much greater than their separation r0{displaystyle r_{0}}, it can be shown that\u03d5=\u03d50+V02r02cos\u2061(\u03a9t)(x2\u2212y2){displaystyle phi =phi _{0}+{frac {V_{0}}{2r_{0}^{2}}}cos(Omega t)(x^{2}-y^{2})!} .Since the electric field is given by the gradient of the potential, we get thatE=\u2212V0r02cos\u2061(\u03a9t)(xe^x\u2212ye^y){displaystyle mathbf {E} =-{frac {V_{0}}{r_{0}^{2}}}cos(Omega t)(xmathbf {hat {e}} _{x}-ymathbf {hat {e}} _{y})!} .Defining \u03c4=\u03a9t\/2{displaystyle tau =Omega t\/2}, the equations of motion in the xy{displaystyle xy}-plane are a simplified form of the Mathieu equation,d2xid\u03c42=\u22124eV0Mr02\u03a92cos\u2061(2\u03c4)xi{displaystyle {frac {d^{2}x_{i}}{dtau ^{2}}}=-{frac {4eV_{0}}{Mr_{0}^{2}Omega ^{2}}}cos(2tau )x_{i}!} .Penning Trap[edit]  The radial trajectory of an ion in a Penning trap; the ratio of cyclotron frequency to magnetron frequency is \u03c9c\/\u03c9m=10\/1{displaystyle omega _{c}\/omega _{m}=10\/1}.A standard configuration for a Penning trap consists of a ring electrode and two end caps. A static voltage differential between the ring and end caps confines ions along the axial direction (between end caps). However, as expected from Earnshaw’s theorem, the static electric potential is not sufficient to trap an ion in all three dimensions. To provide the radial confinement, a strong axial magnetic field is applied.For a uniform electric field E=Ee^x{displaystyle mathbf {E} =Emathbf {hat {e}} _{x}}, the force F=eE{displaystyle mathbf {F} =emathbf {E} } accelerates a positively charged ion along the x{displaystyle x}-axis. For a uniform magnetic field B=Be^z{displaystyle mathbf {B} =Bmathbf {hat {e}} _{z}}, the Lorentz force causes the ion to move in circular motion with cyclotron frequency\u03c9c=eBM{displaystyle omega _{c}={frac {eB}{M}}!} .Assuming an ion with zero initial velocity placed in a region with E=Ee^x{displaystyle mathbf {E} =Emathbf {hat {e}} _{x}} and B=Be^z{displaystyle mathbf {B} =Bmathbf {hat {e}} _{z}}, the equations of motion arex=E\u03c9cB(1\u2212cos\u2061(\u03c9ct)){displaystyle x={frac {E}{omega _{c}B}}(1-cos(omega _{c}t))!} ,y=\u2212E\u03c9cB(\u03c9ct\u2212sin\u2061(\u03c9ct)){displaystyle y=-{frac {E}{omega _{c}B}}(omega _{c}t-sin(omega _{c}t))!} ,z=0{displaystyle z=0!} .The resulting motion is a combination of oscillatory motion around the z{displaystyle z}-axis with frequency \u03c9c{displaystyle omega _{c}} and a drift velocity in the y{displaystyle y}-direction. The drift velocity is perpendicular to the direction of the electric field.For the radial electric field produced by the electrodes in a Penning trap, the drift velocity will precess around the axial direction with some frequency \u03c9m{displaystyle omega _{m}}, called the magnetron frequency. An ion will also have a third characteristic frequency \u03c9z{displaystyle omega _{z}} between the two end cap electrodes. The frequencies usually have widely different values with \u03c9z\u226a\u03c9mc{displaystyle omega _{z}ll omega _{m}     (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki43\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki43\/ion-trap-wikipedia\/#breadcrumbitem","name":"Ion trap – Wikipedia"}}]}]