Keith Mack
The Child-Langmuir law, also known as Child's law, was first proposed by Clement D. Child in 1911. It states that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode is directly proportional to the three-halves power of the anode voltage and inversely proportional to the square of the distance between the cathode and anode. Irving Langmuir discovered the same principle independently and published it in 1913, extending it to cylindrical cathodes and anodes. Child's law was further generalized by Buford R. Conley in 1995 for non-zero velocity at the cathode surface.
| Characteristics | Values |
|---|---|
| First Proposed By | Clement D. Child |
| First Proposed In | 1911 |
| Equation Also Known As | Three-Halves-Power Law |
| Equation First Used For | Giving the space-charge-limited current in a vacuum diode with electrode spacing d |
| Equation First Published By | Irving Langmuir |
| Equation First Published In | 1913 |
| Equation Extended By | Irving Langmuir |
| Equation Extended For | Cylindrical cathodes and anodes |
| Equation Extended In | 1913 |
| Equation Generalized By | Buford R. Conley |
| Equation Generalized For | The case of non-zero velocity at the cathode surface |
| Equation Generalized In | 1995 |
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What You'll Learn
- Child's Law was first proposed by Clement D. Child in 1911
- Irving Langmuir discovered the law independently and published it in 1913
- Child's Law was further generalized by Buford R. Conley in 1995
- Child and Langmuir studied space charge-limited emission for two infinite parallel plane electrodes
- Child-Langmuir Law is also known as the three-halves-power law
Child's Law was first proposed by Clement D. Child in 1911
Child's Law, also known as the Child–Langmuir Law, was first proposed by American physicist and educator Clement D. Child in 1911. Child's Law is an equation that describes the electric current that flows between the plates of a vacuum tube.
The equation is written as:
> J={I/S}={4ε0/9}√{2e/me}{V3/2}/d2
Where m_e is the mass of an electron.
Child's Law states that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage (V) and inversely as the square of the distance (d) separating the cathode and the anode. Child originally derived this equation for the case of atomic ions, which have much smaller ratios of their charge to their mass.
Child's Law was further generalized by Buford R. Conley in 1995 for the case of non-zero velocity at the cathode surface. The application of Child's Law to electron currents was made in 1913 by Irving Langmuir, who extended it to the case of cylindrical cathodes and anodes.
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Irving Langmuir discovered the law independently and published it in 1913
Irving Langmuir, born in Brooklyn, New York, on January 31, 1881, was an American chemist, physicist, and metallurgical engineer. He was awarded the Nobel Prize in Chemistry in 1932 for his work in surface chemistry. Langmuir's most famous publication is the 1919 article "The Arrangement of Electrons in Atoms and Molecules," in which he outlined his "concentric theory of atomic structure."
Langmuir discovered Child-Langmuir Law independently and published it in 1913. Child's law, first proposed by Clement D. Child in 1911, states that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage and inversely as the square of the distance separating the cathode and the anode. Langmuir published the application of this law to electron currents and extended it to the case of cylindrical cathodes and anodes.
Langmuir's early education was influenced by his parents, who encouraged him to carefully observe nature and keep detailed records of his observations. He also had an older brother, Arthur Langmuir, who was a research chemist and encouraged Irving's curiosity about nature and how things work. Langmuir's hobbies included mountaineering, skiing, piloting his plane, and classical music.
Before graduating high school from Chestnut Hill Academy in 1898, Langmuir attended schools in Brooklyn, Philadelphia, and Paris. He then graduated with a Bachelor of Science degree in metallurgical engineering from Columbia University School of Mines in 1903. Langmuir earned his PhD in 1906 from the University of Göttingen, where he studied with physical chemist Walther Nernst. His doctoral thesis was on the "Partial Recombination of Dissolved Gases During Cooling."
Langmuir's initial contributions to science came from his study of light bulbs, which was a continuation of his PhD work. He made significant improvements to the diffusion pump, leading to the invention of the high-vacuum rectifier and amplifier tubes. He also discovered that the lifetime of a tungsten filament could be extended by filling the bulb with an inert gas, such as argon, a critical factor overlooked by other researchers.
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Child's Law was further generalized by Buford R. Conley in 1995
Child's Law, first proposed by Clement D. Child in 1911, states that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage and inversely as the square of the distance separating the cathode and the anode. Child's Law was further generalized by Buford R. Conley in 1995 for the case of non-zero velocity at the cathode surface. This generalization was significant for the theoretical modelling of ion propulsion systems, particularly those operating in the rarefied conditions of low Earth orbit.
Conley's thesis, titled "Utilization of Ambient Gas as a Propellant for Low Earth Orbit Electric Propulsion", was published in May 1995 as part of his Master's degree at the Massachusetts Institute of Technology. The thesis led to the development of the ramjet ion rocket engine, which operates based on the principle of using residual gases in the atmosphere as propellant. This concept, known as atmosphere-breathing electric propulsion or air-breathing electric propulsion (ABEP), eliminates the need for on-board propellant in spacecraft operating in low orbits.
Conley's generalization of Child's Law is expressed in the following equation:
{\displaystyle {I}={\frac {2\varepsilon _{0}m}{9qd^{2}}}\left(\left.\nu _{\text{initial}}^{3/2}-\left(\nu _{\text{initial}}^{2}+{\frac {2qV}{m}}\right)^{3/4}\right)\right)^{2}}
Where {\displaystyle \nu _{\text{initial}}} is the initial velocity of the particle. This equation reduces to Child's Law for the special case of zero initial velocity.
The Child–Langmuir law is a well-known formula that has been extended and built upon over the years. It has been applied in various contexts, including the electron needle problem and patchy emission theories. The law has also been analysed in one, two, and three dimensions, providing valuable insights into the behaviour of charged particles.
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Child and Langmuir studied space charge-limited emission for two infinite parallel plane electrodes
The classical 1D Child-Langmuir law describes the maximum sheet and line current. The Child-Langmuir law is obtained for electrodes with a potential difference separated by a distance. The limiting current is formulated in terms of an integral equation and is solved iteratively to recover the classical one-dimensional Child-Langmuir law.
Child's law, first proposed by Clement D. Child in 1911, states that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage and inversely as the square of the distance separating the cathode and the anode. Irving Langmuir published the application to electron currents in 1913, extending it to cylindrical cathodes and anodes.
The Child-Langmuir law is different from the Mott-Gurney law, which assumes steady-state drift transport and strong scattering. Child's law was further generalized by Buford R. Conley in 1995 for the case of non-zero velocity at the cathode surface. The Child-Langmuir law is important for understanding the behaviour of various practical devices, such as high-current diodes, vacuum and solid-state microelectronic devices, quantum diodes, and semiconductors.
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Child-Langmuir Law is also known as the three-halves-power law
The Child-Langmuir Law, also known as the three-halves-power law, is a fundamental principle in plasma physics that describes the behaviour of current density in a planar vacuum tube diode. It was first proposed by Clement D. Child in 1911 and further developed by Irving Langmuir in 1913. Child's original formulation stated that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode is directly proportional to the three-halves power of the anode voltage and inversely proportional to the square of the distance between the cathode and anode. This equation was derived for atomic ions, which have smaller ratios of their charge to their mass. Langmuir later extended this work to electron currents and cylindrical cathodes and anodes.
The Child-Langmuir Law is a well-known and widely applied concept in plasma physics. It is unique in that it assumes ballistic transport, meaning no collisions or scattering of particles. This assumption sets it apart from other theories, such as the Mott-Gurney law, which assumes steady-state drift transport and strong scattering. The Child-Langmuir Law has been further generalised and studied in one, two, and three dimensions, providing valuable insights into electron behaviour.
The law has been expressed mathematically in various forms, including the classical 1D Child-Langmuir Law, the microscopic Child-Langmuir Law, and extensions to consider patchy emission, electron sheets, and electron needles. These mathematical formulations often involve solving complex nonlinear differential equations, but novel approaches have been developed to estimate space-charge-limited currents without the need for such equations.
The Child-Langmuir Law has been a subject of ongoing research and refinement, with recent studies focusing on electron motion inside planar vacuum tube diodes and the dynamics of charge within them. These investigations have led to a better understanding of the underlying physics and the development of the microscopic Child-Langmuir Law, which is valid for both classical and relativistic regimes.
In summary, the Child-Langmuir Law, also known as the three-halves-power law, is a fundamental concept in plasma physics that describes the relationship between current density and voltage in a planar vacuum tube diode. It has been a subject of extensive study and has provided valuable insights into the behaviour of electrons and the dynamics of charge.
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Frequently asked questions
Clement D. Child first proposed the law in 1911.
Irving Langmuir discovered the law independently and published it in 1913.
Child-Langmuir Law states that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage and inversely as the square of the distance separating the cathode and the anode.
The equation is also known as the "three-halves-power law".
For electrons, the current density J (amperes per meter squared) is written: J= {I/S}= {4ε0/9}√{2e/me}{V3/2/d2}.
