Charged particle drift | (2022)

In many cases of practical interest, the motion in a magnetic field of an electrically charged particle (such as an electron or ion in a plasma) can be treated as the superposition of a relatively fast circular motion around a point called the guiding center and a relatively slow drift of this point. The drift speeds may differ for various species depending on their charge states, masses, or temperatures, possibly resulting in electric currents or chemical separation.


  • 1 Gyration
  • 2 Parallel motion
  • 3 General force drifts
    • 3.1 Gravitational field
    • 3.2 Electric field
    • 3.3 Nonuniform E
  • 4 Nonuniform B
    • 4.1 Grad-B drift
    • 4.2 Curvature drift
    • 4.3 Inertial drift
    • 4.4 Curved vacuum drift
  • 5 Polarization drift
  • 6 Diamagnetic drift
  • 7 Drift Currents
  • 8 References
    • 8.1 External links


If the magnetic field is uniform, the particle velocity is perpendicular to the field, and other forces and fields are absent, then the magnetic Lorentz force is perpendicular to both the velocity and the magnetic field and is constant in magnitude, resulting in particle motion at constant speed on a circular path. This is known as the gyration around the magnetic field. For mass m, charge q, and magnetic field B, the frequency of the circular motion, the gyro-frequency or cyclotron frequency, is

\(\omega_{c} = qB/m . \,\!\)

For speed v, the radius of the orbit, called the gyro-radius or Larmor radius, is

\(r_{L} = v / \omega_{\mbox{c}} . \,\!\)

Parallel motion

Since the magnetic Lorentz force is always perpendicular to the magnetic field, it has no influence (to lowest order) on the parallel motion. In a uniform field with no additional forces, a charged particle will gyrate around the magnetic field according to the perpendicular component of its velocity and drift parallel to the field according to its initial parallel velocity, resulting in a helical orbit. If there is a force with a parallel component, the particle and its guiding center will be correspondingly accelerated.

(Video) ExB drift of a charged particle in an electromagnetic filed

If the field has a parallel gradient, a particle with a finite Larmor radius will also experience a force in the direction away from the larger magnetic field. This effect is known as the magnetic mirror. While it is closely related to guiding center drifts in its physics and mathematics, it is nevertheless considered to be distinct from them.

General force drifts

Generally speaking, when there is a force on the particles perpendicular to the magnetic field, then they drift in a direction perpendicular to both the force and the field. If \(\vec{F}\) is the force on one particle, then the drift velocity is

\(\vec{v}_f = \frac{1}{q} \frac{\vec{F}\times\vec{B}}{B^2}\).

These drifts, in contrast to the mirror effect and the non-uniform B drifts, do not depend on finite Larmor radius, but are also present in cold plasmas. This may seem counterintuitive. If a particle is stationary when a force is turned on, where does the motion perpendicular to the force come from and why doesn’t the force produce a motion parallel to itself? The answer is the interaction with the magnetic field. The force initially results in an acceleration parallel to itself, but the magnetic field deflects the resulting motion in the drift direction. Once the particle is moving in the drift direction, the magnetic field deflects it back against the external force, so that the average acceleration in the direction of the force is zero. There is, however, a one-time displacement in the direction of the force equal to (f/mc-2, which should be considered a consequence of the polarization drift (see below) while the force is being turned on. The resulting motion is a cycloid. More generally, the superposition of a gyration and a uniform perpendicular drift is a trochoid.

All drifts may be considered special cases of the force drift, although this is not always the most useful way to think about them. The obvious cases are electric and gravitational forces. The grad-B drift can be considered to result from the force on a magnetic dipole in a field gradient. The curvature, inertia, and polarisation drifts result from treating the acceleration of the particle as fictitious forces. The diamagnetic drift can be derived from the force due to a pressure gradient. Finally, other forces such as radiation pressure and collisions also result in drifts.

Gravitational field

A simple example of a force drift is a plasma in a gravitational field, e.g. the ionosphere. The drift velocity is

\(\vec{v}_g = \frac{m}{q} \frac{\vec{g}\times\vec{B}}{B^2}\)

Because of the mass dependence, the gravitational drift for the electrons can normally be ignored.

(Video) Lecture 3 -Guiding centre, E X B drift, drift in a general force

The dependence on the charge of the particle implies that the drift direction is opposite for ions as for electrons, resulting in a current. In a fluid picture, it is this current crossed with the magnetic field that provides that force counteracting the applied force.

Electric field

This drift, often called the \(\vec{E}\times\vec{B}\) (E-cross-B) drift, is a special case because the force on the particles depends on their charge. As a result, ions (of whatever mass and charge) and electrons both move in the same direction at the same speed, so there is no net current (assuming quasineutrality). In the context of special relativity, in the frame moving with this velocity, the electric field vanishes. The value of the drift velocity is given by

\(\vec{v}_E = \frac{\vec{E}\times\vec{B}}{B^2}\)

Nonuniform E

If the electric field is not uniform, the above formula is modified to read

\(\vec{v}_E = \left( 1 + \frac{1}{4}r_L^2\nabla^2 \right) \frac{\vec{E}\times\vec{B}}{B^2}\)

Nonuniform B

Guiding center drifts may also result not only from external forces but also from non-uniformities in the magnetic field. It is convenient to express these drifts in terms of the parallel and perpendicular energies

\(\epsilon_\| = \frac{1}{2}mv_\|^2\)
\(\epsilon_\perp = \frac{1}{2}mv_\perp^2\)

In that case, the explicit mass dependence is eliminated. If the ions and electrons have similar temperatures, then they also have similar, though oppositely directed, drift velocities.

Grad-B drift

When a particle moves into a larger magnetic field, the curvature of its orbit becomes tighter, transforming the otherwise circular orbit into a cycloid. The drift velocity is

(Video) 1e Particle motion in given electromagnetic fields: the drifts

\(\vec{v}_{\nabla B} = \frac{\epsilon_\perp}{qB} \frac{\vec{B}\times\nabla B}{B^2}\)

Curvature drift

In order for a charged particle to follow a curved field line, it needs a drift velocity out of the plane of curvature to provide the necessary centripetal force. This velocity is

\(\vec{v}_R = \frac{2\epsilon_\|}{qB}\frac{\vec{R}_c\times\vec{B}}{R_c^2 B}\)

Inertial drift

A more general form of the curvature drift is the inertial drift, given by

\(\vec{v}_{\rm inertial} = \frac{v_\|}{\omega_c}\, \vec{b}\times\frac{d\vec{b}}{dt}\),

where \(\vec{b}=\vec{B}/B\) is the unit vector in the direction of the magnetic field. This drift can be decomposed into the sum of the curvature drift and the term

\(\frac{v_\|}{\omega_c}\, \vec{b}\times\left[\frac{\partial\vec{b}}{\partial t} + (\vec{v}_E\cdot\nabla\vec{b})

In the important limit of stationary magnetic field and weak electric field, the inertial drift is dominated by the curvature drift term.

Curved vacuum drift

In the limit of small plasma pressure, Maxwell’s equations provide a relationship between gradient and curvature that allows the previous two drifts to be combined as follows

\(\vec{v}_R + \vec{v}_{\nabla B} = \frac{2\epsilon_\|+\epsilon_\perp}{qB}\frac{\vec{R}_c\times\vec{B}}{R_c^2 B}\)

For a species in thermal equilibrium, \(2\epsilon_\|+\epsilon_\perp\) can be replaced by \(2k_BT\) (\(k_BT/2\) for \(\epsilon_\|\) and \(k_BT\) for

(Video) Lecture 10 9 Motion of charged particles, Drift

Polarization drift

A time-varying electric field also results in a drift given by

\(\vec{v}_p = \frac{m}{qB^2}\frac{d\vec{E}}{dt}\)

Obviously this drift is different from the others in that it cannot continue indefinitely. Normally an oscillatory electric field results in a polarization drift oscillating 90 degrees out of phase. Because of the mass dependence, this effect is also called the inertia drift. Normally the polarization drift can be neglected for electrons because of their relatively small mass.

Diamagnetic drift

The diamagnetic drift is not actually a guiding center drift. A pressure gradient does not cause any single particle to drift. Nevertheless, the fluid velocity is defined by counting the particles moving through a reference area, and a pressure gradient results in more particles in one direction than in the other. The net velocity of the fluid is given by

\(\vec{v}_D = -\frac{\nabla p\times\vec{B}}{qn B^2}\)

Drift Currents

With the important exception of the E-cross-B drift, the drift velocities of different species will be different. The differential velocity of charged particles results in a current, while the mass dependence of the drift velocity can result in chemical separation.


Cosmic Plasma (1981), Hannes Alfvén

External links


What do you mean by drift of a charged particle? ›

The average velocity of charged particles in a material due to an electric field is known as drift velocity.

What is drift velocity of charged particle? ›

In physics, a drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero.

What happens when a charged particle is moving? ›

Moving charged particles create a magnetic force field. Accelerating charged particles produce changing electric and magnetic force fields which propagate as EM waves. EM radiation that has all the electric and magnetic field variations along the same plane is polarized.

What causes a charged particle to move? ›

Magnetic force can cause a charged particle to move in a circular or spiral path. Cosmic rays are energetic charged particles in outer space, some of which approach the Earth. They can be forced into spiral paths by the Earth's magnetic field. Protons in giant accelerators are kept in a circular path by magnetic force.

What is called drift? ›

A drift is a movement away from somewhere or something, or a movement towards somewhere or something different. ... the drift towards the cities. Synonyms: shift, movement, flow, transfer More Synonyms of drift.

What is drift in simple words? ›

to move slowly, especially as a result of outside forces, with no control over direction: No one noticed that the boat had begun to drift out to sea. A mist drifted in from the marshes.

What is drift current formula? ›

the drift current density due to the translational force exerted by the electric field on the charged particles,(13.77b)J_α,drift=qμαel|zα|nαE_; From: A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences, 2019.

What is called drift velocity? ›

Drift velocity is the average velocity with which electrons 'drift' in the presence of an electric field. It's the drift velocity (or drift speed) that contributes to the electric current. In contrast, thermal velocity causes random motion resulting in collisions with metal ions. Created by Mahesh Shenoy.

What is the drift of electric charge? ›

Drift current is the electric current caused by particles getting pulled by an electric field. The term is most commonly used in the context of electrons and holes in semiconductors, although the same concept also applies to metals, electrolytes, and so on.

What is the movement of charged particles called? ›

Electric current is therefore a flow of charged particles or charge carriers. The charge carrier can be an electron, a proton, an ion, or any particle with charge. In an electric circuit, the charge is usually carried by electrons.

What is a moving charge called? ›

Electric Current

This has units of coulombs per second, which is given its own name: amperes or amps.

What direction do charged particles move? ›

Negative charges and positive charges move in opposite directions. For instance, if the field is into this page, then the positive charges will move counterclockwise and the negative charges will move clockwise.

Is it possible that a charged particle free to move? ›

A charged particle free to move in an electric field always move along an electric line of force.

What are the two types of drift? ›

Types of drift

There are two kinds of spray drift — vapor drift and particle drift.

What is drift process? ›

1. What is process drift? An unintended deviation of the process from the desired setting and performance parameters. This may result in product or process characteristics being outside of documented requirements or specifications.

What causes a drift? ›

Drifting and pulling is often caused by uneven tire pressure. When the tires on one side of the vehicle are underinflated, your vehicle will drift in that direction. The easiest way to fix this is to inflate all of your tires to the appropriate air pressure.

What is drift used for? ›

Drift facilitates communication with website visitors in real-time to help generate leads and improve sales opportunities. The AI-enabled solution comes with a chatbot to automate marketing pipelines and increase customer engagement.

How many types of drift are there? ›

We define three types of drift: asymptoting, overshooting and inverse drift (away from the long-term bias). Precipitation almost always has an asymptoting drift. Temperatures on the other hand, vary between the two forecasting systems, where one tends to overshoot and the other to have an inverse drift.

Which current is called drift? ›

The ocean water current which flow slowly is called Drift. They are affected by atmospheric circulation and the wind belts. When the wind blows over the sea's surface in one direction for a period of time, the stress force produced by friction between the air and the sea water cause the sea water to flow.

What is drift in electrons? ›

Ans: When an electrical field is applied over electrons, they randomly and slowly move from one direction to the other. The net velocities by which the electrons move are defined as electron drift.

What is the difference between drift and current? ›

Difference between Drifts, Current and Streams

The forward movement of surface water of the oceans under the influence of prevailing winds is called drift whereas the ocean current involves the movement of Oceanic water in a definite direction with greater velocity.

What is called zero drift? ›

Zero drift or bias describes the effect where the zero reading of an instrument is modified by a change in ambient conditions. This causes a constant error that exists over the full range of measurement of the instrument. The mechanical form of a bathroom scale is a common example of an instrument prone to zero drift.

How is drift classified? ›

Concept drift types according to Gama et al.

(A) Sudden/Abrupt, (B) incremental, (C) gradual, (D) re-occuring.

What is another name for drift theory? ›

Today, the theory of continental drift has been replaced by the science of plate tectonics. The theory of continental drift is most associated with the scientist Alfred Wegener.

What keeps electrons from drifting? ›

What keeps electrons from drifting away from the nucleus in an atom? A strong nuclear force holds the electrons and protons together. Electrons are attracted to each other. Gravity holds all of the subatomic particles of atoms together.

What is a drift motion? ›

On the other hand (and this is a remarkable peculiarity of charged particle motion in a magnetic field), a force acting at right angles to the field gives rise to particle motion in a direction perpendicular both to the forces and the magnetic field. This motion is known as a drift.

What are the 3 types of charges? ›

Examples of the types of charges are subatomic particles or the particles of matter: Protons are positively charged. Electrons are negatively charged. Neutrons have zero charge.

What are the two types of charges called? ›

Electric charges are of two general types: positive and negative. Two objects that have an excess of one type of charge exert a force of repulsion on each other when relatively close together.

What is the difference between static and moving charge? ›

The most significant difference between the static electricity and the current electricity is that in that static electricity the charges are at rest and they are accumulated on the surface of the insulator, whereas, in current electricity the electrons are in state of motion inside the conductor.

What is the difference between static charge and moving charge? ›

Static electricity is caused by the accumulation of charges on the surface of an item, known as an insulator, whereas current electricity is caused by the movement of charge through an object, known as a conductor.

Will a charged particle always move in direction of electric field? ›

A charged particle always move in the direction of electric field.

Do charged particles flow in the same direction? ›

Direct current (DC) is an electric current that is unidirectional, so the flow of charge is always in the same direction. As opposed to alternating current, the direction and amperage of direct currents do not change.

Does charge have a direction? ›

Recapping, you can find the direction of the electric field created by a charge since positive charges create fields that point radially away from them. And negative charges create fields that point radially toward them.

What do you mean by drift of electrons? ›

Ans: When an electrical field is applied over electrons, they randomly and slowly move from one direction to the other. The net velocities by which the electrons move are defined as electron drift.

What do you mean by drift in electronics? ›

Negatively charged electrons move towards the positive side of the applied voltage while positively charged holes move towards the negative side. This movement or flow of the charge carriers due to applied voltage is called drift.

What is meant by drift in chemistry? ›

in scanning tunneling microscopy or atomic force microscopy, movement of the sample surface with respect to a microscope tip or cantilever due to a lack of thermal equilibrium. [ SEMATECH]

What is meant by drift in time series? ›

Abstract: Time series forecasting is a problem with many applications. However, in many domains, such as stock market, the underlying generating process of the time series observations may change, making forecasting models obsolete. This problem is known as Concept Drift.

What's the difference between a current and a drift? ›

The main difference between longshore current and longshore drift is that longshore currents are the ocean waves that travel parallel to the beach whereas longshore drift is the transportation of sediments along a coast, parallel to the shoreline.

What is drift in static characteristics? ›

Drift. Drift is the change in instrument output over time - when the true value is constant.

What is accuracy and drift? ›

If the model prediction is inaccurate, the transaction is marked as drifted. The Estimated accuracy is then calculated as the fraction of non-drifted transactions to the total number of transactions analyzed. The Base accuracy is the accuracy of the model on the test data.

What is the drift method? ›

Drift method

A variation on the naïve method is to allow the forecasts to increase or decrease over time, where the amount of change over time (called the drift) is set to be the average change seen in the historical data.

How do you know if data is drifting? ›

How to Detect Data Drift? To detect data drift, several methods such as comparing the distributions of the dataset features using statistical tests are available. The python library Eurybia uses a method consisting in training a binary classification model (named “datadrift classifier”).


1. Magnetism. Charged particle drift
(Handy Physicist)
2. Motion of Charge Particle in Cross Electric and Magnetic field ( E×B drift )
(Naimur Rahaman)
3. Shock Drift Acceleration (SDA)
(NASA Video)
4. 2.4 Non Uniform Electric Field lecture no. 17 F.Chen Plasma physics
(Learn Daily Physics)
5. 620 - Motion of charged particles in perpendicular electric and magnetic fields.
(Alexander C)
6. 2.2.2 Centre Guiding Drift Velocity lecture no.12 plasma F.chen
(Learn Daily Physics)

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