Penning trap
Encyclopedia
Penning traps are devices for the storage of charged particles using a homogeneous static magnetic field
and a spatially inhomogeneous static electric field
. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particle
s which have electric charge
. Recently this trap has been used in the physical realization of quantum computation and quantum information processing as well. The Penning trap has also been used in the realization of what is known as a geonium atom
. Currently Penning traps are used in many laboratories worldwide. For example, they are used at CERN
to store antiproton
s.
(1894–1953) by Hans Georg Dehmelt
who built the first trap. Dehmelt got inspiration from the vacuum gauge built by F. M. Penning where a current through a discharge tube in a magnetic field is proportional to the pressure. Citing from H. Dehmelt's autobiography:
H. Dehmelt shared the Nobel Prize in Physics
in 1989 for the development of the ion trap technique.
to confine particles radially and a quadrupole electric field
to confine the particles axially. The static electric potential can be generated using a set of three electrode
s: a ring and two endcaps. In an ideal Penning trap the ring and endcaps are hyperboloids of revolution. For trapping of positive (negative) ions, the endcap electrodes are kept at a positive (negative) potential relative to the ring. This potential produces a saddle point
in the centre of the trap, which traps ions along the axial direction. The electric field causes ions to oscillate (harmonically in the case of an ideal Penning trap) along the trap axis. The magnetic field in combination with the electric field causes charged particles to move in the radial plane with a motion which traces out an epitrochoid
.
The orbital motion of ions in the radial plane is composed of two modes
at frequencies which are called the magnetron
and the modified cyclotron 
frequencies. These motions are similar to the deferent and epicycle
, respectively, of the Ptolemaic model of the solar system.
The sum of these two frequencies is the cyclotron frequency, which depends only on the ratio of electric charge
to mass
and on the strength of the magnetic field
. This frequency can be measured very accurately and can be used to measure the masses of charged particles. Many of the highest-precision mass measurements (masses of the electron
, proton, 2H
, 20Ne
and 28Si
) come from Penning traps.
Buffer gas
cooling, resistive cooling, and laser cooling
are techniques to remove energy from ions in a Penning trap.
Buffer gas cooling relies on collisions between the ions and neutral gas molecules that bring the ion energy closer the energy of the gas molecules.
In resistive cooling, moving image charges
in the electrodes are made to do work through an external resistor, effectively removing energy from the ions.
Laser cooling
can be used to remove energy from some kinds of ions in Penning traps. This technique requires ions with an appropriate electronic structure.
Radiative cooling is the process by which the ions lose energy by creating electromagnetic waves by virtue of their acceleration in the magnetic field. This process dominates the cooling of electrons in Penning traps, but is very small and usually negligible for heavier particles.
Using the Penning trap can have advantages over the radio frequency
trap (Paul trap). Firstly, in the Penning trap only static fields are applied and
therefore there is no micro-motion and resultant heating of the ion due to the
dynamic fields. Also, the Penning trap can be made larger whilst maintaining strong
trapping. The trapped ion can then be held further away from the electrode
surfaces. Interaction with patch potentials on the electrode surfaces can be responsible
for heating and decoherence effects and these effects scale as a high power
of the inverse distance between the ion and the electrode.
(also known as Fourier transform mass spectrometry), is a type of mass spectrometry
used for determining the mass-to-charge ratio
(m/z) of ions based on the cyclotron frequency of the ions in a fixed magnetic field. The ions are trapped in a Penning trap where they are excited to a larger cyclotron radius by an oscillating electric field perpendicular to the magnetic field. The excitation also results in the ions moving in phase (in a packet). The signal is detected as an image current on a pair of plates which the packet of ions passes close to as they cyclotron. The resulting signal is called a free induction decay (fid), transient or interferogram that consists of a superposition of sine waves. The useful signal is extracted from this data by performing a Fourier transform
to give a mass spectrum
.
Single ions can be investigated in a Penning trap held at a temperature of 4 K. For this the ring electrode is segmented and opposite electrodes are connected to a superconducting coil and the source and the gate of a field effect transistor. The coil and the parasitic capacitances of the circuit form a LC circuit
with a Q of about 50 000. The LC circuit is excited by an external electric pulse. The segmented electrodes couple the motion of the single electron to the LC circuit. Thus the energy in the LC circuit in resonance with the ion slowly oscillates between the many electrons (10000) in the gate of the field effect transistor and the single electron. This can be detected in the signal at the drain of the field effect transistor.
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
and a spatially inhomogeneous static electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particle
Subatomic particle
In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...
s which have electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
. Recently this trap has been used in the physical realization of quantum computation and quantum information processing as well. The Penning trap has also been used in the realization of what is known as a geonium atom
Geonium atom
A Geonium atom is a false "atom" created in a magnetic Penning trap. A Penning trap is a combination of a homogeneous magnetic field and an electrostatic quadrupole potential. A single charged particle can be trapped indefinitely in a Penning trap...
. Currently Penning traps are used in many laboratories worldwide. For example, they are used at CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
to store antiproton
Antiproton
The antiproton is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy....
s.
History
The Penning Trap was named after F. M. PenningFrans Michel Penning
Frans Michel Penning was a Dutch physicist. The Penning trap, used for storing charged particles, as well as the Penning mixture and Penning effect of gas discharge tubes are named after him. He also invented a type of cold cathode vacuum gauge known as Penning gauge.-External links:*...
(1894–1953) by Hans Georg Dehmelt
Hans Georg Dehmelt
Hans Georg Dehmelt is a German-born American physicist, who co-developed the ion trap technique with Wolfgang Paul, for which they shared one-half of the Nobel Prize in Physics in 1989...
who built the first trap. Dehmelt got inspiration from the vacuum gauge built by F. M. Penning where a current through a discharge tube in a magnetic field is proportional to the pressure. Citing from H. Dehmelt's autobiography:
"I began to focus on the magnetron/Penning discharge geometry, which, in the Penning ion gauge, had caught my interest already at Göttingen and at Duke. In their 1955 cyclotron resonance work on photoelectrons in vacuum Franken and Liebes had reported undesirable frequency shifts caused by accidental electron trapping. Their analysis made me realize that in a pure electric quadrupole field the shift would not depend on the location of the electron in the trap. This is an important advantage over many other traps that I decided to exploit. A magnetron trap of this type had been briefly discussed in J.R. Pierce's 1949 book, and I developed a simple description of the axial, magnetron, and cyclotron motions of an electron in it. With the help of the expert glassblower of the Department, Jake Jonson, I built my first high vacuum magnetron trap in 1959 and was soon able to trap electrons for about 10 sec and to detect axial, magnetron and cyclotron resonances. " – H. Dehmelt
H. Dehmelt shared the Nobel Prize in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
in 1989 for the development of the ion trap technique.
How it works
Penning traps use a strong homogeneous axial magnetic fieldMagnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
to confine particles radially and a quadrupole electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
to confine the particles axially. The static electric potential can be generated using a set of three electrode
Electrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...
s: a ring and two endcaps. In an ideal Penning trap the ring and endcaps are hyperboloids of revolution. For trapping of positive (negative) ions, the endcap electrodes are kept at a positive (negative) potential relative to the ring. This potential produces a saddle point
Saddle point
In mathematics, a saddle point is a point in the domain of a function that is a stationary point but not a local extremum. The name derives from the fact that in two dimensions the surface resembles a saddle that curves up in one direction, and curves down in a different direction...
in the centre of the trap, which traps ions along the axial direction. The electric field causes ions to oscillate (harmonically in the case of an ideal Penning trap) along the trap axis. The magnetic field in combination with the electric field causes charged particles to move in the radial plane with a motion which traces out an epitrochoid
Epitrochoid
An epitrochoid is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle....
.
The orbital motion of ions in the radial plane is composed of two modes
Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies...
at frequencies which are called the magnetron
and the modified cyclotron frequencies. These motions are similar to the deferent and epicycleDeferent and epicycle
In the Ptolemaic system of astronomy, the epicycle was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets...
, respectively, of the Ptolemaic model of the solar system.
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
to mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
and on the strength of the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. This frequency can be measured very accurately and can be used to measure the masses of charged particles. Many of the highest-precision mass measurements (masses of the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
, proton, 2H
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
, 20Ne
Neon
Neon is the chemical element that has the symbol Ne and an atomic number of 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in either low-voltage neon glow lamps or...
and 28Si
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
) come from Penning traps.
Buffer gas
Buffer gas
A buffer gas is an inert or nonflammable gas. In the Earth's atmosphere, nitrogen acts as a buffer gas. A buffer gas adds pressure to a system and controls the speed of combustion with any oxygen present...
cooling, resistive cooling, and laser cooling
Laser cooling
Laser cooling refers to the number of techniques in which atomic and molecular samples are cooled through the interaction with one or more laser light fields...
are techniques to remove energy from ions in a Penning trap.
Buffer gas cooling relies on collisions between the ions and neutral gas molecules that bring the ion energy closer the energy of the gas molecules.
In resistive cooling, moving image charges
Method of image charges
The method of image charges is a basic problem-solving tool in electrostatics...
in the electrodes are made to do work through an external resistor, effectively removing energy from the ions.
Laser cooling
Laser cooling
Laser cooling refers to the number of techniques in which atomic and molecular samples are cooled through the interaction with one or more laser light fields...
can be used to remove energy from some kinds of ions in Penning traps. This technique requires ions with an appropriate electronic structure.
Radiative cooling is the process by which the ions lose energy by creating electromagnetic waves by virtue of their acceleration in the magnetic field. This process dominates the cooling of electrons in Penning traps, but is very small and usually negligible for heavier particles.
Using the Penning trap can have advantages over the radio frequency
trap (Paul trap). Firstly, in the Penning trap only static fields are applied and
therefore there is no micro-motion and resultant heating of the ion due to the
dynamic fields. Also, the Penning trap can be made larger whilst maintaining strong
trapping. The trapped ion can then be held further away from the electrode
surfaces. Interaction with patch potentials on the electrode surfaces can be responsible
for heating and decoherence effects and these effects scale as a high power
of the inverse distance between the ion and the electrode.
Fourier transform mass spectrometry
Fourier transform ion cyclotron resonance mass spectrometryMass spectrometry
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...
(also known as Fourier transform mass spectrometry), is a type of mass spectrometry
Mass spectrometry
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...
used for determining the mass-to-charge ratio
Mass-to-charge ratio
The mass-to-charge ratio ratio is a physical quantity that is widely used in the electrodynamics of charged particles, e.g. in electron optics and ion optics. It appears in the scientific fields of lithography, electron microscopy, cathode ray tubes, accelerator physics, nuclear physics, Auger...
(m/z) of ions based on the cyclotron frequency of the ions in a fixed magnetic field. The ions are trapped in a Penning trap where they are excited to a larger cyclotron radius by an oscillating electric field perpendicular to the magnetic field. The excitation also results in the ions moving in phase (in a packet). The signal is detected as an image current on a pair of plates which the packet of ions passes close to as they cyclotron. The resulting signal is called a free induction decay (fid), transient or interferogram that consists of a superposition of sine waves. The useful signal is extracted from this data by performing a Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
to give a mass spectrum
Mass spectrum
A mass spectrum is an intensity vs. m/z plot representing a chemical analysis. Hence, the mass spectrum of a sample is a pattern representing the distribution of ions by mass in a sample. It is a histogram usually acquired using an instrument called a mass spectrometer...
.
Single ions can be investigated in a Penning trap held at a temperature of 4 K. For this the ring electrode is segmented and opposite electrodes are connected to a superconducting coil and the source and the gate of a field effect transistor. The coil and the parasitic capacitances of the circuit form a LC circuit
LC circuit
An LC circuit, also called a resonant circuit or tuned circuit, consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C...
with a Q of about 50 000. The LC circuit is excited by an external electric pulse. The segmented electrodes couple the motion of the single electron to the LC circuit. Thus the energy in the LC circuit in resonance with the ion slowly oscillates between the many electrons (10000) in the gate of the field effect transistor and the single electron. This can be detected in the signal at the drain of the field effect transistor.