CN111697307B - Artificial local surface plasmon resonator applied to gyrotron and control method - Google Patents

Artificial local surface plasmon resonator applied to gyrotron and control method Download PDF

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CN111697307B
CN111697307B CN202010466425.7A CN202010466425A CN111697307B CN 111697307 B CN111697307 B CN 111697307B CN 202010466425 A CN202010466425 A CN 202010466425A CN 111697307 B CN111697307 B CN 111697307B
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surface plasmon
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local surface
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CN111697307A (en
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杜朝海
李思琦
朱娟峰
张子文
李繁弘
刘濮鲲
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Peking University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P7/00—Resonators of the waveguide type
    • H01P7/06—Cavity resonators
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    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J23/00—Details of transit-time tubes of the types covered by group H01J25/00
    • H01J23/16—Circuit elements, having distributed capacitance and inductance, structurally associated with the tube and interacting with the discharge
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Abstract

The invention discloses an artificial local surface plasmon resonance cavity applied to a gyrotron and a control method. The invention applies the artificial local surface plasmon resonance cavity to the interaction cavity of the gyrotron, the artificial local surface plasmon resonance cavity is an inward opening circular symmetric grating, and when the structural parameters of the inward opening circular symmetric grating are determined, the resonance frequency is solved through calculation; the stop band and the quasi-pass band are obtained according to the resonance frequency, so that the frequency of the high-order electromagnetic working mode is in the quasi-pass band, and the frequency of the high-order harmonic state is in the stop band, thereby fundamentally eliminating the mode competition problem; and the size of the internally-opened circularly symmetric grating is set and the harmonic frequency is selected according to the actually required resonance frequency.

Description

Artificial local surface plasmon resonator applied to gyrotron and control method
Technical Field
The invention relates to a gyrotron technology, in particular to an artificial local surface plasmon resonator applied to a gyrotron and a control method thereof.
Background
The gyrotron works based on the relativistic electron cyclotron pulse plug principle, adopts the interaction of a fast wave mode and a cyclotron electron beam, can generate high-stability coherent electromagnetic radiation in a millimeter wave and even terahertz frequency band, and can be applied to heating of controllable thermonuclear reaction, imaging of dynamic nuclear polarization nuclear magnetic resonance and wireless communication. The reason why the gyrotron can generate high-power high-frequency electromagnetic waves is that an external strong magnetic field provides inherent gyrotron frequency for electron beams, so that the gyrotron electron beams can interact with the electromagnetic waves in an interaction structure to realize energy conversion.
The gyrotron comprises a launching gun, an interaction cavity, a collector and an energy output structure, and is arranged under an external magnetic field. The electron beam moves spirally in the interaction cavity under the action of an external magnetic field, and if the working frequency of the gyrotron is high enough, the electromagnetic field formed in the interaction cavity by the interaction of the electron beam and the electromagnetic field is a high-order electromagnetic working mode. The working state of the gyrotron is that the electron beam rotates for one circle in the interaction cavity, and if the electromagnetic field resonates once, the electron beam rotates for one circle in the interaction cavity, the working state of the gyrotron is the fundamental wave working state; if the electromagnetic field resonates for multiple times, the electron beam rotates for one circle in the interaction cavity, and the working state of the gyrotron is a higher harmonic working state.
The interaction cavity of the prior gyrotron adopts a circular waveguide resonant cavity. When the frequency of the gyrotron reaches a terahertz frequency band, the interaction cavity of the gyrotron generally adopts a high-order electromagnetic working mode due to the fact that the wavelength and the size of the resonant cavity are in a transition property. The reasons are three points: firstly, the size of the interaction cavity is increased, and the mechanical processing is facilitated; second, increasing the power capacity of the interaction chamber; third, ohmic losses of the interaction chamber are reduced, increasing the quality factor. From the ECO conditions: when the gyrotron works in a fundamental wave mode, the working frequency of the gyrotron is in direct proportion to the intensity of the external magnetic field, namely the higher the working frequency is, the higher the intensity of the external magnetic field is required to be. For example, a gyrotron with a frequency of 100GHz requires a magnetic field of about 3.5T, while a gyrotron with an operating frequency of 400GHz requires a magnetic field of up to 14T, which is assisted by a superconducting magnet, and thus the magnetic field is an important factor for the miniaturization of the gyrotron. The higher harmonic working state is a breakthrough for reducing the requirement of a magnetic field of the terahertz gyrotron, and when the gyrotron works in s-th harmonic, the required magnetic field is 1/s of the magnetic field when the gyrotron works in fundamental wave, so that the requirement on the working magnetic field can be greatly reduced. Therefore, the terahertz gyrotron adopting the high-frequency structure of the circular waveguide resonant cavity generally works in a higher harmonic state, and mainly adopts second harmonic, so that the application of high-resolution dynamic nuclear polarization nuclear magnetic resonance, terahertz imaging detection and other systems is promoted.
However, mode competition is caused by the high-order working mode and the high-order harmonic working state of the gyrotron. The same cyclotron harmonic may excite a plurality of modes with similar working frequencies; meanwhile, different cyclotron harmonics can excite different modes, and the frequencies of the competitive modes are approximately in a frequency doubling relation. Mode competition causes an unstable multimode competition behavior of the electron cyclotron maser system, and the excited competition mode can seriously influence or inhibit the interaction between a normal working mode and an electron beam, so that the working efficiency of a gyrotron is reduced, the working stability is seriously influenced, and the system is caused to generate incoherent electromagnetic radiation. In order to inhibit the problem of mode competition, researchers have proposed a plurality of solutions, such as optimally designing a high-frequency interaction structure, and effectively inhibiting the mode competition by coaxial slotting, confocal waveguide, photonic crystal and other interaction circuits.
Disclosure of Invention
The invention provides an artificial local surface plasmon resonator applied to a gyrotron and a control method thereof, and the artificial local surface plasmon resonator is based on a metal strip and an ultrathin grating structure and can realize sub-wavelength control of a wave beam.
One objective of the present invention is to provide an artificial local surface plasmon resonator applied to a gyrotron.
The invention relates to an artificial local surface plasmon resonance cavity applied to a gyrotron, which is used as an interaction cavity of the gyrotron and comprises the following components: an inward opening circularly symmetric grating formed in the metal substrate; wherein the material of the metal substrate is an ideal electric conductor PEC; forming an air cavity by forming a through hole with the radius r in the center of the metal substrate; forming a periodic fan-shaped groove with the depth of h along the circumferential radial direction around the air cavity, wherein h is R-R to form an internally-opened circularly symmetric grating; the inner radius of the internally-opened circularly symmetric grating is R, the outer radius of the internally-opened circularly symmetric grating is R, the grating constant is d, the grating thickness is a, the grating duty ratio is a/d, the grating number is N, and the number relation Nd-2 pi R is satisfied; according to the approximate conditions of professor Pendri of empire university[1]The grating constant satisfies the sub-wavelength limit d < lambda0，λ0The wavelength corresponding to the eigenfrequency of the artificial local surface plasmon resonant cavity; a uniform and strong magnetic field is externally applied along the radial direction of the artificial local surface plasmon resonant cavity, an electron beam is incident to the artificial local surface plasmon resonant cavity along the radial direction, the electron beam spirally moves in the artificial local surface plasmon resonant cavity under the action of the magnetic field, and the mode of an electromagnetic field formed by the interaction of the electron beam and the magnetic field is uniformly distributed along the axial direction; the eigen equation of the artificial local surface plasmon resonant cavity is as follows:
Figure GDA0003151620150000021
wherein, JmM-order form, J ', of Bessel function of the first kind'mIn the form of m-th order of the derivative of the Bessel function of the first kind, m being the number of angular modes, k0Is the wave number n in the artificial local surface plasmon resonant cavitygFor the refractive index of air, c is the speed of light, and the functions f and g are expressed as follows:
f＝Y1(k0ngr)J1(k0ngR)-Y1(k0ngR)J1(k0ngr) (2)
g＝Y1(k0ngR)J0(k0ngr)-Y0(k0ngr)J1(k0ngR) (3)
wherein, Y0In the zeroth order form of Bessel functions of the second kind, Y1In the first order form of Bessel functions of the second kind, J0Being a zeroth order form of Bessel function of the first kind, J1Is a first order form of a Bessel function of the first type;
the equation (1) is a transcendental equation, and when the structural parameters of the internally-opened circularly symmetric grating are determined, the resonance frequency of each mode of the artificial local surface plasmon resonant cavity is solved through calculation; the stop band and the quasi-pass band of the gyrotron are obtained according to the resonance frequency of the artificial local surface plasmon resonance cavity, so that the working frequency of the gyrotron is in the quasi-pass band, and meanwhile, the harmonic competition frequency is in the stop band, and the mode competition problem can be fundamentally eliminated; when the inner radius R of the internally-opened circularly symmetric grating is unchanged, the larger the outer radius R is, namely the deeper the grating depth h is, the lower the resonant frequency of each mode is; when the inner radius and the outer radius of the internally-opened circularly symmetric grating are kept unchanged, the larger the duty ratio a/d is, the higher the resonant frequency of each mode is; therefore, the size of the inward opening circularly symmetric grating is set according to the actually required resonance frequency.
The material of the metal substrate adopts copper.
The inner radius of the internally-opened circularly symmetric grating is 0.1-1 mm, the outer radius of the internally-opened circularly symmetric grating is 0.3-3 mm, the duty ratio of the grating is 0.3-0.7, the number of the gratings is more than 60 and less than 200, and the range of the magnetic field intensity is 1-20T. The grating constant satisfies the sub-wavelength limitation d < lambda0I.e. 10d < lambda0。
The invention also aims to provide a control method of the artificial local surface plasmon resonant cavity applied to the gyrotron.
The invention discloses a control method of an artificial local surface plasmon polariton resonant cavity applied to a gyrotron, which comprises the following steps:
1) providing a metal substrate, wherein the material of the metal substrate is an ideal electric conductor PEC;
2) forming an air cavity by forming a through hole with the radius r in the center of the metal substrate; radially inward opening a periodic fan-shaped groove with the depth of h along the circumference at the periphery of the air cavity, wherein h is R-R to form an inward opening circularly symmetric grating; the inner radius of the internally-opened circularly symmetric grating is R, the outer radius of the internally-opened circularly symmetric grating is R, the grating constant is d, the grating duty ratio is a/d, the number of the gratings is N, and the number relation Nd-2 pi R is satisfied; according to the approximate conditions of professor Pendri of empire university [1 ]]The grating constant satisfies the sub-wavelength limit d < lambda0，λ0The wavelength corresponding to the eigenfrequency of the artificial local surface plasmon resonant cavity;
3) a uniform and strong magnetic field is externally applied along the radial direction of the artificial local surface plasmon resonant cavity, an electron beam is incident to the artificial local surface plasmon resonant cavity along the radial direction, the electron beam spirally moves in the artificial local surface plasmon resonant cavity under the action of the magnetic field, and the mode of an electromagnetic field formed by the interaction of the electron beam and the magnetic field is uniformly distributed along the axial direction; the eigen equation of the artificial local surface plasmon resonant cavity is as follows:
Figure GDA0003151620150000031
wherein, JmM-order form, J ', of Bessel function of the first kind'mIn the form of m-th order of the derivative of the Bessel function of the first kind, m being the number of angular modes, k0Is the wave number in the artificial local surface plasmon resonant cavity, c is the speed of light, ngFor the refractive index of air, the functions f and g are expressed as follows:
f＝Y1(k0ngr)J1(k0ngR)-Y1(k0ngR)J1(k0ngr) (2)
g＝Y1(k0ngR)J0(k0ngr)-Y0(k0ngr)J1(k0ngR) (3)
wherein, Y0In the zeroth order form of Bessel functions of the second kind, Y1In the first order form of Bessel functions of the second kind, J0Being a zeroth order form of Bessel function of the first kind, J1Is a first order form of the bessel function of the first kind.
The equation (1) is a transcendental equation, and when the structural parameters are determined, the resonance frequency of each mode of the cross section of the artificial local surface plasmon resonant cavity is solved through calculation;
4) the cutoff frequency of the resonant frequency of the artificial local surface plasmon resonant cavity is equal to the resonant frequency of the section of the artificial local surface plasmon resonant cavity, the gyrotron works in a near cutoff region, and the working frequency of the gyrotron is equal to the resonant frequency of the section of the artificial local surface plasmon resonant cavity, so that the working frequency of the gyrotron is equal to the resonant frequency of the section of the artificial local surface plasmon resonant cavity, and therefore, a stop band and a quasi-pass band of the gyrotron can be obtained according to the resonant frequency of each mode of the section of the artificial local surface plasmon resonant cavity, a high-order electromagnetic working mode and a high-order harmonic working state of the gyrotron are positioned in the quasi-pass band, and a low-order electromagnetic working mode and a low-order harmonic state are positioned in the stop band, so that the problem of mode competition can be fundamentally eliminated;
5) when the inner radius R of the internally-opened circularly symmetric grating is unchanged, the larger the outer radius R is, namely the deeper the grating depth h is, the lower the resonant frequency of each mode is; when the inner radius and the outer radius of the internally-opened circularly symmetric grating are kept unchanged, the larger the duty ratio a/d is, the higher the resonant frequency of each mode is; therefore, the size of the inward opening circularly symmetric grating is set according to the actually required resonance frequency.
The invention further aims to provide an application of the artificial local surface plasmon resonant cavity as an interaction cavity of a gyrotron.
The invention has the advantages that:
the invention applies the artificial local surface plasmon resonance cavity to the interaction cavity of the gyrotron, the artificial local surface plasmon resonance cavity is an inward opening circular symmetric grating, and when the structural parameters of the inward opening circular symmetric grating are determined, the resonance frequency is solved through calculation; the stop band and the quasi-pass band are obtained according to the resonance frequency, so that the frequency of the high-order electromagnetic working mode is in the quasi-pass band, and the frequency of the high-order harmonic state is in the stop band, thereby fundamentally eliminating the mode competition problem; and the size of the internally-opened circularly symmetric grating is set and the harmonic frequency is selected according to the actually required resonance frequency.
Drawings
FIG. 1 is a schematic diagram of one embodiment of an artificial localized surface plasmon resonator for a gyrotron in accordance with the present invention;
FIG. 2 is a TE of an embodiment of an artificial local surface plasmon resonator for a gyrotron of the present inventionn,1、TEn,2And TEn,3A schematic diagram of the resonant frequency of (c);
FIG. 3 is the present inventionTE of one embodiment of the artificial local surface plasmon resonator applied to gyrotronn,1The electric field profile of the pattern;
FIG. 4 is a TE of one embodiment of an artificial local surface plasmon resonator for a gyrotron of the present inventionn,2The electric field profile of the pattern;
FIG. 5 is a TE of one embodiment of an artificial local surface plasmon resonator for a gyrotron of the present inventionn,3The electric field profile of the pattern;
FIG. 6 is a graph of the spectrum of the electromagnetic field in the resonant cavity of one embodiment of an artificial localized surface plasmon resonant cavity for a gyrotron of the present invention;
fig. 7 is an overall schematic diagram of the artificial localized surface plasmon resonator applied to a gyrotron according to the present invention.
Detailed Description
The invention will be further elucidated by means of specific embodiments in the following with reference to the drawing.
As shown in fig. 1, the artificial local surface plasmon resonator applied to a gyrotron of the present embodiment includes: an inward opening circularly symmetric grating formed in the metal substrate; the material of the metal substrate is an ideal electric conductor PEC; forming an air cavity by forming a through hole with the radius r in the center of the metal substrate; radially inward opening a periodic fan-shaped groove with the depth h-R-R along the circumference around the air cavity to form an inward opening circularly symmetric grating; the inner radius of the internally-opened circularly symmetric grating is R, the outer radius of the internally-opened circularly symmetric grating is R, the grating constant is d, the grating duty ratio is a/d, the number of the gratings is N, and the number relation Nd-2 pi R is satisfied. As shown in fig. 7, the artificial local surface plasmon resonator RC serves as an interaction cavity of the gyrotron; and a uniform and strong magnetic field MF is externally applied along the radial direction of the artificial local surface plasmon resonant cavity, and the electron gun EG emits electron beams EB to be incident to the artificial local surface plasmon resonant cavity RC along the radial direction. Approximate conditions according to Pendry[1]The grating constant satisfies the sub-wavelength limit d < lambda0，λ0The wavelength corresponding to the eigenfrequency of the resonator.
In this embodiment, the specific structural parameters are set as follows: n-120And a/d is 0.4, R is 3R, and R is 0.5 mm. Modeling the artificial local surface plasmon resonance cavity in an eigen-mode solver of a CST microwave working chamber, setting the metal substrate as ideal metal, and setting the rest part as vacuum to solve the eigen frequency of the metal substrate. Since the principle of gyrotron is that a cyclotron electron beam interacts with a transverse electric field (TE mode) to exchange energy, the TE mode is the main subject of study. TEn,1、TEn,2And TEn,3The resonant frequencies of the modes are shown in fig. 2, and n is the number of azimuthal modes.
As can be seen from fig. 2, for the same radial mode, the larger the number of angular modes, the higher the resonant frequency, and the smaller the resonant frequency gap between adjacent modes, which finally converges to a frequency value. The larger the number of radial modes, the higher the resonant frequency for different radial modes. With increasing frequency, the appearance of the mode is TE1,1、TE2,1、TE3,1、TE4,1……TE1,2、TE2,2、TE3,2、TE4,2……TE1,3、TE2,3、TE3,3、TE4,3… …, respectively; no resonance frequency exists between 0 and 42.885GHz, so that the frequency band between 0 and 42.885GHz is called as a first stop band; TE1,1、TE2,1、TE3,1、TE4,1……TEn,1The resonant frequency of the mode only appears between 42.885GHz and 60GHz, so that the 42.885 GHz-60 GHz frequency band is called a first quasi-passband; no resonance frequency exists between 60 and 162.662GHz, so that the frequency band between 60 and 162.662GHz is called as a second stop band; TE1,2、TE2,2、TE3,2、TE4,2……TEn,2The resonant frequency of the mode only appears between 162.662GHz and 220GHz, so that the 162.662GHz to 220GHz frequency band is called a second quasi-passband. No resonance frequency exists between 220 and 258.386GHz, so that the frequency band between 220 and 258.386GHz is called as a third stop band; TE1,3、TE2,3、TE3,3、TE4,3……TEn,3The resonant frequency of the mode only appears between 258.386GHz and 370GHz, so that the 258.386GHz to 370GHz frequency band is called a third quasi-passband; this physical phenomenon is called "band gap" of artificial localized surface plasmons,the "quasi-passband" and "stopband" are shown in Table 1 below.
TABLE 1 quasi-passband and stopband frequencies
Figure GDA0003151620150000061
Compare in traditional circular waveguide resonant cavity, artifical local surface plasmon resonant cavity has two advantages: first, there is a "stop band". The resonance frequency of each mode of the cross section of the artificial local surface plasmon resonance cavity is the cut-off frequency of each mode of the artificial local surface plasmon resonance cavity, the gyrotron works in a near cut-off region, the working frequency is close to the cut-off frequency of the artificial local surface plasmon resonance cavity, and therefore the working frequency of the gyrotron is close to the resonance frequency of the cross section of the artificial local surface plasmon resonance cavity. If the competing frequency of the harmonic gyrotron is in the 'stop band' of the resonance frequency, the mode competition problem can be fundamentally eliminated. And no stop band exists in the circular waveguide, the distribution of the eigenfrequency is related to the Bessel function, and the eigenmode exists near any frequency point. Second, for the same radial number, when the angular number n is small (n <3), the interval between adjacent eigenfrequencies is large, and thus setting the operating frequency at a frequency point where the angular number n is small can reduce the mode competition problem.
TEn,1、TEn,2And TEn,3The distribution of the electric field intensity of the three modes is shown in FIGS. 3-5. Therefore, the electric field of the TE mode of the artificial local surface plasmon resonant cavity permeates into the internally-opened circularly symmetric grating, and the electric field in the air cavity is closer to the interface of the grating and the air cavity along with the increase of the number of the angular modes, so that the position of the circle center of the air cavity is almost not distributed by the electric field. Therefore, the mode with lower angular mode number is selected to be more beneficial to the energy exchange between the cyclotron and the electromagnetic wave.
The terahertz harmonic gyrotron is designed by taking the artificial local surface plasmon resonant cavity as an example. TE is selected for use in working mode of terahertz gyrotron2,3Operating frequency of 299.749GHz and electron cyclotron frequency74.94GHz, and therefore operates in the fourth harmonic operating mode. The advantages of such a design are two-fold: the fundamental frequency of the first and the second harmonic waves of the cyclotron electron pulse plug radiation is 74.94GHz, the frequency of the second harmonic wave is 149.87GHz, the frequency of the third harmonic wave is 224.81GHz, the three frequencies are competitive frequencies, but are all positioned in a stop band, the artificial surface plasmon resonant cavity does not have a corresponding eigen mode, and the competitive frequencies lose growth conditions and cannot start oscillation; second, the operating frequency is 299.749GHz, and the competition mode near this frequency is TE of 258.386GHz1,3Mode sum TE of 327.017GHz3,3Modes, but the frequency interval is far, and competition for the working mode is difficult to generate. The specific design parameters are as shown in the following table 2, except that the applied magnetic field must be fixed, other parameters can be adjusted by themselves.
TABLE 2 harmonic gyrotron design parameters
Figure GDA0003151620150000071
A PIC (Particle-in-cell) module of a CST Particle working chamber is utilized to simulate the self-consistent interaction process of electron beams and an electromagnetic field in a harmonic gyrotron resonant cavity based on artificial local surface plasmons, FIG. 6 is a spectrogram of a field in the resonant cavity, f is frequency, and a visible spectrum is relatively pure and has no harmonic competition frequency.
Finally, it is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.
Reference documents:
[1]Pendry J B,Martin-Moreno L,Garcia-Vidal F J.Mimicking Surface Plasmons with Structured Surfaces[J].Science,2004,305(5685):847-848.

Claims (7)

1. person applied to gyrotronThe surface plasmon resonance cavity of worker's local area, its characterized in that, surface plasmon resonance cavity of worker's local area is as the interaction cavity of gyrotron, surface plasmon resonance cavity of worker's local area includes: an inward opening circularly symmetric grating formed in the metal substrate; wherein the material of the metal substrate is an ideal electric conductor PEC; forming an air cavity by forming a through hole with the radius r in the center of the metal substrate; forming a periodic fan-shaped groove with the depth of h along the circumferential radial direction around the air cavity, wherein h is R-R to form an internally-opened circularly symmetric grating; the inner radius of the internally-opened circularly symmetric grating is R, the outer radius of the internally-opened circularly symmetric grating is R, the grating constant is d, the grating thickness is a, the grating duty ratio is a/d, the grating number is N, and the number relation Nd-2 pi R is satisfied; the grating constant satisfies the sub-wavelength limitation d < lambda0，λ0The wavelength corresponding to the eigenfrequency of the artificial local surface plasmon resonant cavity; a uniform and strong magnetic field is externally applied along the radial direction of the artificial local surface plasmon resonant cavity, an electron beam is incident to the artificial local surface plasmon resonant cavity along the radial direction, the electron beam spirally moves in the artificial local surface plasmon resonant cavity under the action of the magnetic field, and the mode of an electromagnetic field formed by the interaction of the electron beam and the magnetic field is uniformly distributed along the axial direction; the eigen equation of the artificial local surface plasmon resonant cavity is as follows:
Figure FDA0003179593000000011
wherein, JmM-order form, J ', of Bessel function of the first kind'mIn the form of m-th order of the derivative of the Bessel function of the first kind, m being the number of angular modes, k0Is the wave number n in the artificial local surface plasmon resonant cavitygFor the refractive index of air, c is the speed of light, and the functions f and g are expressed as follows:
f＝Y1(k0ngr)J1(k0ngR)-Y1(k0ngR)J1(k0ngr) (2)
g＝Y1(k0ngR)J0(k0ngr)-Y0(k0ngr)J1(k0ngR) (3)
wherein, Y0In the zeroth order form of Bessel functions of the second kind, Y1In the first order form of Bessel functions of the second kind, J0Being a zeroth order form of Bessel function of the first kind, J1Is a first order form of a Bessel function of the first type;
the equation (1) is a transcendental equation, and when the structural parameters of the internally-opened circularly symmetric grating are determined, the resonance frequency of each mode of the artificial local surface plasmon resonant cavity is solved through calculation; the stop band and the quasi-pass band of the gyrotron are obtained according to the resonance frequency of the artificial local surface plasmon resonance cavity, so that the working frequency of the gyrotron is in the quasi-pass band, and meanwhile, the harmonic competition frequency is in the stop band, and the mode competition problem can be fundamentally eliminated; when the inner radius R of the internally-opened circularly symmetric grating is unchanged, the larger the outer radius R is, namely the deeper the grating depth h is, the lower the resonant frequency of each mode is; when the inner radius and the outer radius of the internally-opened circularly symmetric grating are kept unchanged, the larger the duty ratio a/d is, the higher the resonant frequency of each mode is; therefore, the size of the inward opening circularly symmetric grating is set according to the actually required resonance frequency.
2. The artificial local surface plasmon resonator of claim 1 wherein the metal substrate is copper.
3. The artificial local surface plasmon resonance cavity of claim 1, wherein the circularly symmetric grating has an inner radius R of 0.1 to 1mm, an outer radius R of 0.3 to 3mm, a grating duty cycle a/d of 0.3 to 0.7, and a number of gratings of 60 < N < 200.
4. A control method of an artificial local surface plasmon resonator applied to a gyrotron as claimed in claim 1, wherein said control method comprises the steps of:
1) providing a metal substrate, wherein the material of the metal substrate is an ideal electric conductor PEC;
2) forming an air cavity by forming a through hole with the radius r in the center of the metal substrate; radially inward opening a periodic fan-shaped groove with the depth of h along the circumference at the periphery of the air cavity, wherein h is R-R to form an inward opening circularly symmetric grating; the inner radius of the internally-opened circularly symmetric grating is R, the outer radius of the internally-opened circularly symmetric grating is R, the grating constant is d, the grating duty ratio is a/d, the number of the gratings is N, and the number relation Nd-2 pi R is satisfied; the grating constant satisfies the sub-wavelength limitation d < lambda0，λ0The wavelength corresponding to the eigenfrequency of the artificial local surface plasmon resonant cavity;
3) a uniform and strong magnetic field is externally applied along the radial direction of the artificial local surface plasmon resonant cavity, an electron beam is incident to the artificial local surface plasmon resonant cavity along the radial direction, the electron beam spirally moves in the artificial local surface plasmon resonant cavity under the action of the magnetic field, and the mode of an electromagnetic field formed by the interaction of the electron beam and the magnetic field is uniformly distributed along the axial direction; the eigen equation of the artificial local surface plasmon resonant cavity is as follows:
Figure FDA0003179593000000021
wherein, JmM-order form, J ', of Bessel function of the first kind'mIn the form of m-th order of the derivative of the Bessel function of the first kind, m being the number of angular modes, k0Is the wave number in the artificial local surface plasmon resonant cavity, c is the speed of light, ngFor the refractive index of air, the functions f and g are expressed as follows:
f＝Y1(k0ngr)J1(k0ngR)-Y1(k0ngR)J1(k0ngr) (2)
g＝Y1(k0ngR)J0(k0ngr)-Y0(k0ngr)J1(k0ngR) (3)
wherein, Y0In the zeroth order form of Bessel functions of the second kind, Y1In the first order form of Bessel functions of the second kind, J0Being a zeroth order form of Bessel function of the first kind, J1Is a first order form of a Bessel function of the first type;
the equation (1) is a transcendental equation, and when the structural parameters are determined, the resonance frequency of each mode of the cross section of the artificial local surface plasmon resonant cavity is solved through calculation;
4) the cutoff frequency of the resonance frequency of the artificial localized surface plasmon resonance cavity is equal to the resonance frequency of the section of the artificial localized surface plasmon resonance cavity, the gyrotron works in a near cutoff region, and the working frequency of the gyrotron is equal to the resonance frequency of the section of the artificial localized surface plasmon resonance cavity, so that a stop band and a quasi-pass band of the gyrotron can be obtained according to the resonance frequency of each mode of the section of the artificial localized surface plasmon resonance cavity, a high-order electromagnetic working mode and a high-order harmonic working state of the gyrotron are positioned in the quasi-pass band, and a low-order electromagnetic working mode and a low-order harmonic state are positioned in the stop band, thereby fundamentally eliminating the problem of mode competition;
5) when the inner radius R of the internally-opened circularly symmetric grating is unchanged, the larger the outer radius R is, namely the deeper the grating depth h is, the lower the resonant frequency of each mode is; when the inner radius and the outer radius of the internally-opened circularly symmetric grating are kept unchanged, the larger the duty ratio a/d is, the higher the resonant frequency of each mode is; therefore, the size of the inward opening circularly symmetric grating is set according to the actually required resonance frequency.
5. The control method according to claim 4, wherein the metal substrate is made of copper.
6. The control method according to claim 4, wherein the circularly symmetric grating has an inner radius R of 0.1 to 1mm, an outer radius R of 0.3 to 3mm, a grating duty ratio a/d of 0.3 to 0.7, and a number of gratings of 60 < N < 200.
7. An application method of an artificial local surface plasmon resonator as an interaction cavity of a gyrotron is characterized in thatThe artificial local surface plasmon resonant cavity comprises: an inward opening circularly symmetric grating formed in the metal substrate; wherein the material of the metal substrate is an ideal electric conductor PEC; forming an air cavity by forming a through hole with the radius r in the center of the metal substrate; forming a periodic fan-shaped groove with the depth of h along the circumferential radial direction around the air cavity, wherein h is R-R to form an internally-opened circularly symmetric grating; the inner radius of the internally-opened circularly symmetric grating is R, the outer radius of the internally-opened circularly symmetric grating is R, the grating constant is d, the grating thickness is a, the grating duty ratio is a/d, the grating number is N, and the number relation Nd-2 pi R is satisfied; the grating constant satisfies the sub-wavelength limitation d < lambda0，λ0The wavelength corresponding to the eigenfrequency of the artificial local surface plasmon resonant cavity; a uniform and strong magnetic field is externally applied along the radial direction of the artificial local surface plasmon resonant cavity, an electron beam is incident to the artificial local surface plasmon resonant cavity along the radial direction, the electron beam spirally moves in the artificial local surface plasmon resonant cavity under the action of the magnetic field, and the mode of an electromagnetic field formed by the interaction of the electron beam and the magnetic field is uniformly distributed along the axial direction; the eigen equation of the artificial local surface plasmon resonant cavity is as follows:
Figure FDA0003179593000000031
wherein, JmM-order form, J ', of Bessel function of the first kind'mIn the form of m-th order of the derivative of the Bessel function of the first kind, m being the number of angular modes, k0Is the wave number n in the artificial local surface plasmon resonant cavitygFor the refractive index of air, c is the speed of light, and the functions f and g are expressed as follows:
f＝Y1(k0ngr)J1(k0ngR)-Y1(k0ngR)J1(k0ngr) (2)
g＝Y1(k0ngR)J0(k0ngr)-Y0(k0ngr)J1(k0ngR) (3)
wherein, Y0In the zeroth order form of Bessel functions of the second kind, Y1In the first order form of Bessel functions of the second kind, J0Being a zeroth order form of Bessel function of the first kind, J1Is a first order form of a Bessel function of the first type;
the equation (1) is a transcendental equation, and when the structural parameters of the internally-opened circularly symmetric grating are determined, the resonance frequency of each mode of the artificial local surface plasmon resonant cavity is solved through calculation; the stop band and the quasi-pass band of the gyrotron are obtained according to the resonance frequency of the artificial local surface plasmon resonance cavity, so that the working frequency of the gyrotron is in the quasi-pass band, and meanwhile, the harmonic competition frequency of the gyrotron is in the stop band, thereby fundamentally eliminating the problem of mode competition; when the inner radius R of the internally-opened circularly symmetric grating is unchanged, the larger the outer radius R is, namely the deeper the grating depth h is, the lower the resonant frequency of each mode is; when the inner radius and the outer radius of the internally-opened circularly symmetric grating are kept unchanged, the larger the duty ratio a/d is, the higher the resonant frequency of each mode is; therefore, the size of the inward opening circularly symmetric grating is set according to the actually required resonance frequency.
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