KR101223811B1 - Enhancement of coherence in relativistic nonlinear Thomson scattering and generation of high power ultrashort X-ray pulse using nanotube or nanowire target and sharply increasing laser pulse - Google Patents

Abstract

The present invention relates to a novel method for generating high-power ultra-short X-rays, and is intended to simultaneously satisfy the density and thickness conditions of the target and the angular conditions of the laser, the target, and the detector for generating microwaves in the Atosecond unit.
According to the present invention, a groundbreaking method for clearly and directly observing a phenomenon such as a chemical reaction occurring in a very short time of less than femtosecond is proposed.

Description

Enhancement of coherence in relativistic nonlinear Thomson scattering and generation of high power ultrashort X-ray pulse using nanotube or nanowire target and sharply increasing laser pulse}

The present invention relates to a method for generating high power ultra-short X-rays by applying a laser of rapidly increasing intensity to a nanotube.

Ultrashort pulses are a clear and direct way to see what happens in a very short time.

According to the phenomenon to be observed, pulses of various wavelengths and lengths are required. FIG. 1 shows extremely short pulses developed to date according to photon energy and length. Typically, femtosecond lasers based on Ti: Sapphire can be used to identify the temporal changes and intermediate processes of chemical reactions.

In 1999, Ahmed Zewail of CALTECH won the Nobel Prize for Chemistry for the observation of chemical reactions using femtosecond lasers. Among the methods for generating pulses shorter than 1 femtosecond, the presently implemented method is high-order harmonic generation by the interaction of an inert gas and a femtosecond laser. The shortest X-ray pulse generated by this method is about 80 attoseconds ( ^10-18 seconds) long.

In this method, because there is a limit on the intensity of the laser that can be used, a relatively weak laser is used, and there is a limit on the intensity of the ultrashort pulses generated.

On the other hand, a method of using an X-ray free electron laser (X-ray Free Electron Laser) is also proposed to generate a strong X-ray pulse of less than 1 femtosecond. The method is expected to generate about 300 Atoseconds of X-rays, with the disadvantage of requiring hundreds of billions of construction costs and several kilometers of space.

Relativistic nonlinear Thomson scattering (RNTS) has been proposed as a method of generating Atosecond X-ray pulses as a powerful laser-electron reaction. When the stationary electron reacts with the laser, the electron vibrates by the electric field of the laser. The accelerated charges emit electromagnetic waves, which are called thomson scattering, and the emission of electromagnetic waves and reactions with electromagnetic waves such as lasers.

When the intensity of the laser is small, the electrons are accelerated in proportion to the laser electric field, and the emission of electromagnetic waves also has a linear relationship with the electric field of the laser.

이상), 아인슈타인 상대성 이론에 따라 전자의 속도가 빛의 속도 이상으로 가속될 수 없기 때문에 속도가 커질수록 전자 질량이 증가하여 가속도는 줄어들게 된다.
If the laser is counted, the electrons vibrate and move forward under the influence of the magnetic field. When the intensity of the laser reaches the relativistic region (approximately 2 X with laser wavelength 800 nm)

Since the velocity of electrons cannot be accelerated beyond the speed of light according to the Einstein theory of relativity, the higher the velocity, the greater the mass of the electron and the acceleration is reduced.

Therefore, the acceleration is easy while the electron is slow, but the acceleration is slowed while the speed is close to the speed of light. As a result, it is known that the former has a serrated motion (Fig. 2).

At this time, Atosecond X-ray pulses such as (a) and (b) of FIG. 3 are emitted at a specific angle. As the speed of electrons approaches the speed of light, light emission is concentrated in the direction of the electrons, so that strong X-ray pulses can be used without additional focusing.

Although the generation of Atosecond X-ray pulses through relativistic nonlinear thomson scattering is simple when there is one electron, general electrons exist in the form of an electron beam or plasma, so in order to actually generate an Atosecond pulse, coherence conditions must be satisfied.

That is, even if each electron generates an Atosecond pulse, if the electrons that do not satisfy the coherence condition are distributed over a wide area, the pulse width becomes longer by the length of the electron distribution as shown in FIG.

In addition, as shown in FIG. 3 (c), only photons of much lower energy are generated, not X-rays. A mirror condition as shown in FIG. 4 has been proposed as a method of coherence of attosecond pulses generated by various electrons.

Referring to FIG. 4, electrons are distributed in a thin film target having a thickness of several nanometers, and an angle at which a laser is incident and an angle at which a generated pulse is measured may be related to an incident angle and a reflection angle of a mirror around the target, respectively. At that time (mirror condition is established), coherence condition is established, and at this time, Atocho X-ray pulse is generated. At this time, for all the electrons on the target when the mirror condition is satisfied, the sum of the time when the laser pulse reaches the electron and the time when the Atosecond pulse generated by the electron reaches the detector is equal.

Coherence conditions are essential for generating Atocho X-ray spreads through relativistic nonlinear thomson scattering, and mirror conditions using thin film targets have been proposed to satisfy the coherence conditions.

When the thin film and the strong laser react, the Lorentz force causes the electrons to be accelerated to the speed of light in the direction of the laser, and the ions, which are several thousand to tens of thousands of times heavier than the electrons, hardly move.

In order to satisfy the mirror condition, the thickness of the electrons constituting the target must be maintained at several nanometers during the reaction with the laser. A target composed only of electrons away from ions has a very high electron density and repulsive force by Coulomb force. This is strong and increases in thickness at a rapid rate. As the thickness of the electrons increases, coherence is not maintained. Therefore, a method of maintaining a thin thickness for generating an Atosecond X-ray pulse is required. Also, if the coherence conditions are not met, X-rays with short wavelengths cannot be obtained and the intensity of pulses is very weak.

The problem to be solved in the present invention is to propose a method of generating a high power ultra-short Atosecond X-ray pulse by greatly improving the degree of coherence of relativistic nonlinear Thompson scattering.

In order to achieve the above object, the present invention utilizes a laser condition and a nanotube target of which the intensity increases rapidly, and the geometrical condition can generate a high power ultra-short Atocho X-ray pulse by implementing the device to satisfy the mirror condition. Present the way.

It is known that coherence conditions are essential for generating Atocho X-ray pulses through relativistic nonlinear thomson scattering, and mirror conditions using thin film targets have been proposed to satisfy such coherence conditions.

When the thin film and the strong laser react, the Lorentz force causes the electron to accelerate close to the speed of light in the laser traveling direction. In order to satisfy the mirror condition, the thickness of the electrons constituting the target should be kept very thin, such as several nanometers, during the reaction with the laser. The repulsive force is so strong that the thickness of the electronic layer increases rapidly.

As the thickness of the electronic layer increases, the coherence condition is broken soon, and thus the generation of the Atocho X-ray pulse becomes impossible.

In other words, it is an object of the present invention to effectively implement the coherence condition is to obtain a strong Atosecond X-ray pulse through this.

Means for solving the specific problems will be described in detail with reference to the accompanying drawings.

The method for achieving the coherence condition proposed in the present invention is essential for generating Atosecond X-ray pulses, and the high-power ultra-short X-ray pulses are enabled by the rapidly increasing laser and nanotube targets and mirror conditions of the present invention.

The Atosecond X-ray pulse implemented by the present invention enables a phenomenon occurring within a very short time, for example, real-time observation of a chemical reaction instant.

Although the construction cost of more than 100 billion won and the space securing problem of more than several kilometers, which have been presented as disadvantages in the existing strong X-ray generation method (X-ray free electron laser) of length less than 1 femtosecond, have been unsolved problems for a long time, the present invention All of them can be solved at once by the method proposed in.

값에 따른 스펙트럼을 나타낸 그래프이다.1 shows various ultrashort pulses according to photon energy and pulse length.
Figure 2 (a) is the motion path of electrons reacting with the relativistic laser. The horizontal axis is the direction of travel of the laser and the vertical axis is the position of the polarization direction of the laser.
(B) is the velocity of electrons versus the speed of light over time. Blue represents the polarization (y) direction of the laser, and orange represents the velocity of the laser (x) direction. As the green dashed line approaches the speed of electrons, it can't accelerate anymore.
3 is a spectral diagram of pulses generated by relativistic nonlinear Thompson scattering for a single electron, FIG. 3 (a) and pulse shape FIG. 3 (b), and spectral diagrams of pulses from multiple electrons when no coherence condition is established. 3 (c) and pulse shape are also shown in FIG. 3 (d).
4 shows coherence conditions using target and mirror conditions.
FIG. 5 illustrates the coherent conditions of relativistic nonlinear thomson scattering using laser pulses and nanotube arrays as rapidly increasing intensities. The same effect can be achieved by using nanowires instead of nanotubes.
6 is a general laser pulse and a laser pulse whose intensity increases rapidly.
7 shows coherence enhancement with the use of nanotube targets, rapidly increasing laser pulses. Each graph shows the spectrum of the generated pulses, which are mapped with the vertical axis as density and the intensity of the spectrum as color. Since the same number of electrons is assumed for all densities, the intensity of the spectrum represents the degree of coherence.
8 is a diagram showing the spectrum according to the nanotube diameter.
9 and 10 with respect to the laser pulse width conditions,

It is a graph showing the spectrum according to the value.

Hereinafter, exemplary embodiments will be described with reference to the accompanying drawings.

In summary, the conditions for generating the Atosecond X-ray pulse wave in the present invention are as follows. That is, while satisfying the mirror conditions as shown in FIG. 5, the target is a two-dimensional planar array of nanotubes or nanowires instead of a thin film, which is conventionally presented, but in a Gaussian form in time. It is a technical feature to generate Atosecond X-rays by using a laser pulse whose intensity increases rapidly instead of the general femtosecond laser.

As described above, in order to implement the Atosecond X-ray pulse, which is an object of the present invention, a coincidence condition must be satisfied, and satisfying the mirror condition as shown in FIG. 4 has already been proposed as one of the methods capable of satisfying the coincidence condition.

4 illustrates a coherence condition using a conventional thin film target and a mirror condition. As described above, in the method of using such a thin film as a target, the coherence is broken due to an increase in the target thickness due to the coulomb force. The implementation of X-ray pulses was not possible.

5 is a configuration for relativistic nonlinear thomson scattering that satisfies the mirror conditions proposed in the present invention.

As shown in FIG. 5, the nanotubes (or nanowires), the laser, and the detector are disposed. The path of incidence and the detector position of the laser should be in one plane perpendicular to the longitudinal direction of the target.

Instead of the thin film used as the conventional target of FIG. 4, the target is a two-dimensional planar array of nanotubes or nanowires, and the intensity of the laser pulse is rapidly increased in the present invention instead of a general femtosecond laser pulse having a Gaussian shape over time. A method of using a laser pulse is presented. (See laser of FIG. 6)

First, in the case of the nanotube target, the principle of coherence during the reaction time with the laser is explained by increasing the diameter of the region in which the extruded electron layer is distributed very slowly.

As shown in Figure 5, when using the nanotube target,

(나노튜브의 초기지름),

(초기 전자 밀도)인 상태에서, 레이저 펄스와의 반응으로 인해 나노튜브 지름이 d 로 늘어났을 때 표면에서의 전기장은 아래와 같이 표현된다.

(Initial diameter of nanotube),

In the state of (initial electron density), when the nanotube diameter increases to d due to the reaction with the laser pulse, the electric field at the surface is expressed as follows.

As the diameter of the nanotube increases, the strength of the interelectron repulsion decreases in inverse proportion to the diameter, and the rate at which the diameter increases increases rapidly. This is the main reason for using nanotubes as targets in the present invention.

In addition, laser pulses of rapidly increasing intensity in time are used, and the speed of electrons is increased to higher energy as compared to a laser having a slowly increasing intensity.

According to a special theory of relativity, the faster the particle, the greater its mass, the less the acceleration of electrons, the slower the diameter of the nanotube, and eventually the coherence is achieved.

On the other hand, the same effect can be seen using nanowires instead of nanotubes.

1. Target Density

In order to generate an Atosecond pulse wave, a density condition to be provided by a target is explained below.

)가 0.01*

이상일 경우에 결맞음이 향상되는데,

은 사용된 레이저의 파장이

(단위 :미터)일 때 다음과 같이 표현될 수 있다.Target Density (Number /

) Is 0.01 *

If this is the case, coherence is improved.

Is the wavelength of the laser used

When expressed in meters, it can be expressed as:

는 진공중에서 유전율이고

는 전자의 질량이며, e 는 전자의 전하량 c는 광속이다.

Is the dielectric constant in vacuum

Is the mass of electrons and e is the charge amount c of the electron.

The most general reason why the coherence is improved by the nanotube array target is that electrons are spread out in a direction other than the thickness direction of the target.

In the present invention, due to the limitation of the simulation, only the nanotubes arranged in the direction perpendicular to the plane formed by the laser traveling direction and the detector are shown (see FIG. 5). However, the nanotubes may have angles that are not necessarily in the vertical direction. That is, the nanotubes are shown in the vertical direction for the sake of simulation.

Unlike FIG. 5, the target shape of the present invention may have a net-shaped nanotube target, and even a thin hole-perforated thin film may have the same function if the density condition is satisfied. That is, since the target that is expected to satisfy the density condition most easily with the current technology is a nanotube array, the drawings are presented as nanotubes as shown in FIG. 5.

In other words, the reference to the nanotube array is exemplified only, and other types of targets generated by other methods may be made when the density condition and the mirror condition (angle condition and thickness condition) are satisfied.

In other words, unlike hollow nanotubes, non-empty nanowires and nanorods can be used, and targets made of empty space by lithography or the like can be used on thin films. In another case, a target in which nanotubes are placed on a thin film is also possible as an example of another target.

If the typical thin film thickness is 3 nm and the nanotube diameter is 2 nm, coherence may occur better than a conventional 5 nm thick single thin film (shown in FIG. 4).

Further expansion, a 2 nm deep groove in the 5 nm thin film can also improve coherence than the original 5 nm thin film. Through this groove, the intensity of the pulse becomes stronger in a specific wavelength region.

2. Target thickness condition among mirror conditions

Hereinafter, the thickness condition of the target of the X-ray pulse generator which can satisfy a mirror condition is demonstrated.

The thickness conditions of general mirror conditions are as follows.

That is, the pulse width that can be generated is limited according to the thickness T of the thin film, and the following relationship is established. In the present invention, the diameter d of the nanotube corresponds to the thin film thickness T value. That is, the known general thickness condition is

보다 작거나 같아야 한다는 것이다.

It must be less than or equal to.

Figure 8 shows the spectrum according to the diameter of the nanotubes.

Generally, the wavelength of 10 nm or less, that is, the photon energy of 124 eV or more is called X-ray, but when the diameter of the nanotube is 10 nm or more, the X-ray region becomes very weak in FIG. 8. The upper limit is given in the range of 10 nm or less.

There is no minimum value of diameter for relativistic nonlinear Thomson scattering and coherence, and the smaller the diameter is, the better the physical diameter is, although there is no requirement for the minimum value of the target thickness (the diameter in the case of nanotubes). Since the distance between them is 0.246 nm, there is no nanowire with a diameter of 0.1 nm or less, so the lower limit of the thickness of the target is set to 0.1 nm. Eventually, the thickness condition of the target is set within the range of 0.1 nm to 10 nm.

3. Angle condition of mirror condition

The angle conditions (or position conditions) will be described below.

만큼 기울어진 평면에 배열된다.
Many nanotubes are arranged perpendicular to the direction of laser polarization,

Are arranged in an inclined plane.

는 레이저펄스 진행 방향과 검출기가 이루는 각도이며,

는 레이저 진행 방향과 나노튜브 배열면이 이루는 각도이다. 항상

는

의 두 배가 되도록 유지시켜야 하며, 검출기의 각도 범위가 넓은 경우 슬릿을 통해 검출하는 각도를 제한할 필요가 있다.

Is the angle between the laser pulse traveling direction and the detector.

Is the angle formed by the laser propagation direction and the nanotube array surface. always

The

It should be maintained at twice, and it is necessary to limit the angle of detection through the slit if the detector's angular range is wide.

= 2 x

의 조건이 만족된 상태에서 가장 강한 펄스가 검출되는 각도를 찾는다.

= 2 x

Find the angle at which the strongest pulse is detected when the condition is satisfied.

4. Laser condition

Hereinafter, the conditions of the incident laser will be described. In the present invention, a condition in which the intensity of the laser increases rapidly must be satisfied, and FIG. 6 illustrates a general laser pulse and a laser pulse in which the intensity rapidly increases.

Equation 2 was used in the simulation for determining the laser condition.

는 시간의 함수이며 t가

이하일 때에는

이고 그 이상일 때에는

이다.

이 레이저의 파장일때

,

이다.
here

Is a function of time and t is

If less than

And more than that

to be.

At the wavelength of this laser

,

to be.

One) Laser intensity  And wavelength conditions

Laser intensity and wavelength conditions are as follows.

단위는

이고, 레이저 파장

의 단위는

이다.The intensity of the laser in this expression

Unit is

Laser wavelength

The unit of

to be.

For any laser wavelength, RNTS occurs when the laser intensity satisfies the condition of equation (3).

2) Laser pulse width condition

      Hereinafter, the laser pulse width condition will be described.

The half-width half-maximum (HWHM) of the envelope up to the point where the intensity of the laser pulse is strongest shall be less than one quarter of the laser electromagnetic cycle.

에 해당된다. If the laser pulse follows Equation 2, HWHM

Corresponds to

이상일 경우의

값에 관계없이 발생되는 아토초 펄스는 동일하다.
The pulse width after the laser's strongest point does not affect coherence, so it does not need to be specified. That is, t in Equation 2

When abnormal

Atosecond pulses generated regardless of the value are the same.

To maintain coherence, the intensity of the laser reacting with the target must be weak before generating the RNTS. If the wavelength of the laser is short, the pulse width must be small according to the ratio of the wavelength. Therefore, the pulse width range is defined based on the laser electromagnetic wave period.

의 절반에 해당한다. The HWHM of the envelope of laser intensity, which maintains coherence in the X-ray region when the wavelength of the laser is 800 nm, is 0.6 fs, which is about 1/4 of the laser electromagnetic cycle. If the laser electric field is given by Equation 2, the HWHM of the intensity

Corresponds to half.

값에 따른 스펙트럼을 나타낸 그래프이다.

값이 1.2 fs 보다 길어지면, HWHM 값이 0.6 fs 보다 커지면 X선 영역의 세기가 약해짐을 확인할 수 있다. RNTS가 일어날 정도의 레이저와 타깃이 반응이 일어난 이후에는 더 이상 결맞음이 유지되지 않으므로, 가장 센 부분 이후의 펄스 형태 및 폭은 발생되는 아토초 펄스에 거의 영향을 주지 않는다.
9 and 10 are

It is a graph showing the spectrum according to the value.

If the value is longer than 1.2 fs, the intensity of the X-ray region is weakened when the HWHM value is greater than 0.6 fs. Coherence is no longer maintained after the laser and target to the extent that the RNTS will occur, so the pulse shape and width after the strongest portion have little effect on the generated Atosecond pulses.

5. Simulation Results

On the other hand, Figure 7 is a simulation result of the coherence improvement according to the use of the nanotube target, a rapidly increasing laser pulse.

Each graph shows the spectrum of the generated pulses, which are mapped with the vertical axis as density and the intensity of the spectrum as color. Since the same number of electrons is assumed for all densities, the intensity of the spectrum represents the degree of coherence.

4 described above is a configuration for relativistic nonlinear thomson scattering that satisfies the mirror condition.

As described above, when the thin film is used as a target in this structure, coherence is broken due to an increase in the thickness of the thin film due to the coulomb force. To solve this problem, two-dimensional planar arrays of nanotubes or nanowires were used instead of thin films, and laser pulses of rapidly increasing intensity were used instead of general femtosecond laser pulses having a Gaussian shape over time.

Simulations were performed to test the coherence characteristics of the mirror conditions using the nanotube arrays presented in the present invention. (FIG. 7) A PIC (particle in cell) method was used to simulate the movement of electrons. To obtain the motion of the electrons, we need the Maxwell's equation to calculate the electromagnetic field generated by the laser and the charge, and the relativistic Newton's equation to calculate the movement of the electron under the influence of the generated electromagnetic field.

The PIC method is a numerical calculation of Maxwell's equations and relativistic Newton's equations that accurately describes the relativistic nonlinear thomson scattering by laser and the Coulomb force between electrons or electrons and ions at distances of more than one cell size. The relativistic modified Larmor equation was used to calculate the electromagnetic wave generated from the movement of electrons obtained by the PIC method at the observation position.

FIG. 7 shows the degree of coherence improvement by using a laser pulse whose intensity is rapidly increased in the nanotube target. Each graph shows the spectrum of the generated pulses, mapping with the vertical axis as the density and the intensity of the spectrum as the color.

Since the same number of electrons is assumed for all densities, the intensity of the spectrum represents the degree of coherence. In the case of general laser pulse conditions, the degree of coherence improvement is greater in the case of nanotubes or nanowires than in the case of thin film targets, and when the laser pulses of rapidly increasing intensity are used in the same target condition (nanotubes). It can be seen that the degree of coherence is further improved.

Although the embodiments of the present invention have been described as described above, the scope of the present invention is not limited thereto, but any invention of equivalent level that can be substituted at the level of those skilled in the art is included in the scope of the present invention.

Claims (4)

As a condition of a target for generating an Atocho X-ray by injecting a laser pulse of rapidly increasing intensity into the target,
Target Density (Number /

),
0.01 *

Must be greater than or equal to

And (

: Permittivity in vacuum,

: Electron mass, e: amount of electrons, c: luminous flux,

(Unit: meter): wavelength of laser)
The thickness of the target,

Satisfies a condition that must be less than or equal to,
The target is from the incident laser direction

Arranged in an inclined plane by

Is the angle between the laser pulse traveling direction and the detector.

Is the angle of laser travel and the angle

The

Satisfies twice the angle of

The incident laser intensity and wavelength are

(Intensity of laser:

(

), Laser wavelength:

(

Satisfies)),
Atosecond X-rays are generated by satisfying a condition in which the half-width half-maximum (HWHM) of the envelope is less than 1/4 of the laser electromagnetic wave period in the laser pulse and its envelope. doing,
(Where the highest point of the envelope height is the envelope maximum, half of this value is half maximum, and the HWHM (half-width maximum) is the time when the maximum Time interval between time)

A method of generating high power ultra-short X-ray pulses using a laser pulse that is rapidly increasing in intensity.
The method according to claim 1,
The target is characterized in that the nanotubes or nanowires,
A method of generating high power ultra-short X-ray pulses using a laser pulse that is rapidly increasing in intensity. The method according to claim 1,
The target is a thin film (thinfilm) formed a predetermined groove using lithography,
A method of generating high power ultra-short X-ray pulses using a laser pulse that is rapidly increasing in intensity. The method according to claim 1,
The target has a thickness of 0.1 to 10 nm, characterized in that
A method of generating high power ultra-short X-ray pulses using a laser pulse that is rapidly increasing in intensity.

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