Введение
Ондулятор – это устройство-вставка из области физики высоких энергий и обычно является частью более крупной установки, такой как синхротронное кольцо хранения, или может быть компонентом лазера на свободных электронах. Он состоит из периодической структуры дипольных магнитов, которые могут быть как постоянными, так и сверхпроводящими. Статическое магнитное поле попеременно изменяется вдоль длины ондулятора с определенной длиной волны. Электроны, проходящие через эту периодическую магнитную структуру, вынуждены совершать колебания и, следовательно, излучать энергию. Излучение, генерируемое в ондуляторе, очень интенсивное и концентрируется в узких энергетических диапазонах спектра, а также коллимировано в плоскости орбиты электронов. Это излучение направляется по линиям пучков для проведения экспериментов в различных областях науки. Параметр силы ондулятора равен:
installation, a synchrotron storage ring, or it may be a component of a free electron laser. It consists of a periodic structure of dipole magnets. These can be permanent magnets or superconducting magnets. The static magnetic field alternates along the length of the undulator with a wavelength Electrons traversing the periodic magnet structure are forced to undergo oscillations and thus to radiate energy. The radiation produced in an undulator is very intense and concentrated in narrow energy bands in the spectrum. It is also collimated on the orbit plane of the electrons. This radiation is guided through beamlines for experiments in various scientific areas. The undulator strength parameter is:
,
where e is the electron charge, B is the magnetic field, is the spatial period of the undulator magnets, is the electron rest mass, and c is the speed of light. This parameter characterizes the nature of the electron motion. For the oscillation amplitude of the motion is small and the radiation displays interference patterns which lead to narrow energy bands. If the oscillation amplitude is bigger and the radiation contributions from each field period sum up independently, leading to a broad energy spectrum. In this regime of fields the device is no longer called an undulator; it is called a wiggler. The key difference between undulator and wiggler is coherence. In the case of an undulator, the emitted radiation is coherent with a wavelength determined by the period length and the beam energy, while in wiggler the electrons are not coherent. The usual description of the undulator is relativistic but classical. This means that although a precise calculation is tedious, the undulator can be seen as a black box, where only functions inside the device affect how an input is converted to an output; an electron enters the box and an electromagnetic pulse exits through a small exit slit. The slit should be small enough such that only the main cone passes, and the side lobes of the wavelength spectra can be ignored. Undulators can provide several orders of magnitude higher flux than a simple bending magnet and as such are in high demand at synchrotron radiation facilities. For an undulator with N periods, the brightness can be up to more than a bending magnet. The first factor of N occurs because the intensity is enhanced up to a factor of N at harmonic wavelengths due to the constructive interference of the fields emitted during the N radiation periods. The usual pulse is a sine with some envelope. The second factor of N comes from the reduction of the emission angle associated with these harmonics, which is reduced as 1/N. When the electrons come with half the period, they interfere destructively, the undulator stays dark. The same is true, if they come as a bead chain. The polarization of the emitted radiation can be controlled by using permanent magnets to induce different periodic electron trajectories through the undulator. If the oscillations are confined to a plane the radiation will be linearly polarized. If the oscillation trajectory is helical, the radiation will be circularly polarized, with the handedness determined by the helix. If the electrons follow the Poisson distribution a partial interference leads to a linear increase in intensity. In the free electron laser the intensity increases exponentially with the number of electrons. An undulator's figure of merit is spectral radiance.
,
installation, a synchrotron storage ring, or it may be a component of a free electron laser. It consists of a periodic structure of dipole magnets. These can be permanent magnets or superconducting magnets. The static magnetic field alternates along the length of the undulator with a wavelength Electrons traversing the periodic magnet structure are forced to undergo oscillations and thus to radiate energy. The radiation produced in an undulator is very intense and concentrated in narrow energy bands in the spectrum. It is also collimated on the orbit plane of the electrons. This radiation is guided through beamlines for experiments in various scientific areas. The undulator strength parameter is:
,
where e is the electron charge, B is the magnetic field, is the spatial period of the undulator magnets, is the electron rest mass, and c is the speed of light. This parameter characterizes the nature of the electron motion. For the oscillation amplitude of the motion is small and the radiation displays interference patterns which lead to narrow energy bands. If the oscillation amplitude is bigger and the radiation contributions from each field period sum up independently, leading to a broad energy spectrum. In this regime of fields the device is no longer called an undulator; it is called a wiggler. The key difference between undulator and wiggler is coherence. In the case of an undulator, the emitted radiation is coherent with a wavelength determined by the period length and the beam energy, while in wiggler the electrons are not coherent. The usual description of the undulator is relativistic but classical. This means that although a precise calculation is tedious, the undulator can be seen as a black box, where only functions inside the device affect how an input is converted to an output; an electron enters the box and an electromagnetic pulse exits through a small exit slit. The slit should be small enough such that only the main cone passes, and the side lobes of the wavelength spectra can be ignored. Undulators can provide several orders of magnitude higher flux than a simple bending magnet and as such are in high demand at synchrotron radiation facilities. For an undulator with N periods, the brightness can be up to more than a bending magnet. The first factor of N occurs because the intensity is enhanced up to a factor of N at harmonic wavelengths due to the constructive interference of the fields emitted during the N radiation periods. The usual pulse is a sine with some envelope. The second factor of N comes from the reduction of the emission angle associated with these harmonics, which is reduced as 1/N. When the electrons come with half the period, they interfere destructively, the undulator stays dark. The same is true, if they come as a bead chain. The polarization of the emitted radiation can be controlled by using permanent magnets to induce different periodic electron trajectories through the undulator. If the oscillations are confined to a plane the radiation will be linearly polarized. If the oscillation trajectory is helical, the radiation will be circularly polarized, with the handedness determined by the helix. If the electrons follow the Poisson distribution a partial interference leads to a linear increase in intensity. In the free electron laser the intensity increases exponentially with the number of electrons. An undulator's figure of merit is spectral radiance.
где e – заряд электрона, B – магнитное поле, λ – пространственный период магнитов ондулятора, m₀ – масса электрона в состоянии покоя, а c – скорость света. Этот параметр характеризует характер движения электрона. При λ/2π << 1 амплитуда колебаний мала, и излучение демонстрирует интерференционные картины, приводящие к узким энергетическим полосам. Если λ/2π >> 1 амплитуда колебаний больше, и вклады излучения от каждого периода поля суммируются независимо, что приводит к широкому энергетическому спектру. В этом режиме поля устройство перестает называться ондулятором и называется виглером. Ключевое различие между ондулятором и виглером заключается в когерентности. В случае ондулятора излучаемое излучение когерентно, с длиной волны, определяемой длиной периода и энергией пучка, в то время как в вигглере электроны не когерентны. Обычно ондулятор описывается релятивистски, но классически. Это означает, что, хотя точный расчет сложен, ондулятор можно рассматривать как «черный ящик», где только функции внутри устройства влияют на преобразование входного сигнала в выходной; электрон входит в ящик, а электромагнитный импульс выходит через небольшую выходную щель. Щель должна быть достаточно мала, чтобы проходил только основной конус, а боковые лепестки спектра длин волн можно игнорировать. Ондуляторы могут обеспечивать на несколько порядков более высокий поток, чем простой отклоняющий магнит, и поэтому пользуются большим спросом в установках синхротронного излучения. Для ондулятора с N периодами яркость может быть до N² раз выше, чем у отклоняющего магнита. Первый множитель N возникает из-за того, что интенсивность увеличивается до N раз на гармонических длинах волн благодаря конструктивной интерференции полей, излучаемых в течение N периодов излучения. Типичный импульс представляет собой синусоиду с некоторой огибающей. Второй множитель N обусловлен уменьшением угла излучения, связанного с этими гармониками, которое уменьшается как 1/N. Когда электроны приходят с фазой, равной половине периода, они интерферируют деструктивно, и ондулятор становится «темным». То же самое верно, если они приходят в виде цепочки частиц. Поляризацию излучаемого излучения можно контролировать, используя постоянные магниты для создания различных периодических траекторий электронов в ондуляторе. Если колебания ограничены плоскостью, излучение будет линейно поляризованным. Если траектория колебаний спиральная, излучение будет циркулярно поляризованным, а его направление определяется направлением спирали. Если электроны следуют распределению Пуассона, частичная интерференция приводит к линейному увеличению интенсивности. В лазере на свободных электронах интенсивность увеличивается экспоненциально с увеличением числа электронов. Показателем качества ондулятора является спектральная яркость.
installation, a synchrotron storage ring, or it may be a component of a free electron laser. It consists of a periodic structure of dipole magnets. These can be permanent magnets or superconducting magnets. The static magnetic field alternates along the length of the undulator with a wavelength Electrons traversing the periodic magnet structure are forced to undergo oscillations and thus to radiate energy. The radiation produced in an undulator is very intense and concentrated in narrow energy bands in the spectrum. It is also collimated on the orbit plane of the electrons. This radiation is guided through beamlines for experiments in various scientific areas. The undulator strength parameter is:
,
where e is the electron charge, B is the magnetic field, is the spatial period of the undulator magnets, is the electron rest mass, and c is the speed of light. This parameter characterizes the nature of the electron motion. For the oscillation amplitude of the motion is small and the radiation displays interference patterns which lead to narrow energy bands. If the oscillation amplitude is bigger and the radiation contributions from each field period sum up independently, leading to a broad energy spectrum. In this regime of fields the device is no longer called an undulator; it is called a wiggler. The key difference between undulator and wiggler is coherence. In the case of an undulator, the emitted radiation is coherent with a wavelength determined by the period length and the beam energy, while in wiggler the electrons are not coherent. The usual description of the undulator is relativistic but classical. This means that although a precise calculation is tedious, the undulator can be seen as a black box, where only functions inside the device affect how an input is converted to an output; an electron enters the box and an electromagnetic pulse exits through a small exit slit. The slit should be small enough such that only the main cone passes, and the side lobes of the wavelength spectra can be ignored. Undulators can provide several orders of magnitude higher flux than a simple bending magnet and as such are in high demand at synchrotron radiation facilities. For an undulator with N periods, the brightness can be up to more than a bending magnet. The first factor of N occurs because the intensity is enhanced up to a factor of N at harmonic wavelengths due to the constructive interference of the fields emitted during the N radiation periods. The usual pulse is a sine with some envelope. The second factor of N comes from the reduction of the emission angle associated with these harmonics, which is reduced as 1/N. When the electrons come with half the period, they interfere destructively, the undulator stays dark. The same is true, if they come as a bead chain. The polarization of the emitted radiation can be controlled by using permanent magnets to induce different periodic electron trajectories through the undulator. If the oscillations are confined to a plane the radiation will be linearly polarized. If the oscillation trajectory is helical, the radiation will be circularly polarized, with the handedness determined by the helix. If the electrons follow the Poisson distribution a partial interference leads to a linear increase in intensity. In the free electron laser the intensity increases exponentially with the number of electrons. An undulator's figure of merit is spectral radiance.
История
Русский физик Виталий Гинзбург теоретически показал в статье 1947 года, что можно построить ондуляторы. Джулиан Швингер опубликовал полезную работу в 1949 году, упростив необходимые вычисления до функций Бесселя, для которых существовали таблицы. Это было существенно для решения уравнений проектирования, так как цифровые компьютеры в то время были недоступны большинству исследователей. Ханс Моц и его коллеги из Стэнфордского университета продемонстрировали первый ондулятор в 1952 году. Он создал первое искусственно полученное когерентное инфракрасное излучение. Конструкция позволяла генерировать широкий диапазон частот, от видимого света до миллиметровых волн.