EP2279650B1 - Device for reducing phase error of a superconducting undulator - Google Patents

Description

The invention relates to a device for reducing the phase error of a superconducting undulator according to the preamble of claim 1.

As in conventional permanent magnet undulators, the quality of the undulator is limited by field errors even in superconducting undulators. The field strengths in the individual periods of the undulator may differ slightly. This forms a phase error that reduces the quality of the photon beam generated in the undulator.

To reduce field errors, as out H. Onuki and P. Elleaume, Undulators, Wigglers and their Applications, Volume 1, Chapter Technology of insertion devices, pp. 148-213, Taylor & Francis, 2003 , and JA Clarke, The Science and Technology of Undulators and Wigglers, Chapter 9 Measurement and Correction of Insertion Devices, pp. 171-176, Oxford Science Publication, 2004 , known, chased conventional permanent magnet undulators . This means that the field errors in the individual periods are compensated by additional elements, in particular plates or additional conductor coils.

For superconducting undulators, conventional shimming, in particular with metal sheets or additional coils, is just as possible. The disadvantage, however, is that the undulator must first be cooled before the existing field of the undulator can be measured. After subsequent warming up of the undulator, shimming of the undulator is carried out while warm. As a check, the undulator must be cooled down afterwards. This procedure is z. B. off S. Prestemon, D. Dietderich, S. Bartlett, M. Coleman, S. Gourlay, A. Lietzke, S. Marks, S. Mattafirri, R. Scanlan, R. Schlueter, B. Wahrer and B. Wang, Design, Fabrication and Test Results of Undulators Using Nb3Sn Superconductor, IEEE Transactions on Applied Superconductivity, Vol. 15, pp. 1236-1239, 2005 , known.

D. Wollmann, A. Bernhard, S. Casalbuoni, M. Hagelstein, B. Kostka, R. Rossmanith, M. Weisser, E. Steffens, G. Gerlach, and T. Baumbach, A concept for electric field error compensation for the ANKA superconducting undulator, Proceedings of EPAC 2006, Edinburgh, Scotland, pp. 3577-3579, 2006 describe a device for reducing the phase error of a superconducting undulator having two rows of juxtaposed magnetic poles, wherein each two adjacent poles in one of the two rows in the sign of their magnetic field differ and the device has at least one closed superconducting loop includes a pole in both rows.

In S. Chouhan, R. Rossmanith, S. Strohmer, D. Doelling, A. Geisler, A. Hobl and S. Kubsky, Field error compensation and thermal beam load in a superconductive undulator, Proceedings of the 2003 Partial Accelerator Conference, p. 899-901, 2003 , and HO Moser and CZ Diao, Finite-length field error and its compensation in superconducting miniundulators, Nucl. Instr. & Meth. In Phys. Res. A 535, pp. 606-613, 2004 , additional superconducting loops are introduced and operated, which complicate the device and require additional space.

Therefore, shimming with additional current-carrying coils that are connected to external power supplies, consuming and expensive. In addition, current-carrying coils can solve the error with reasonable effort only insufficient.

Proceeding from this, it is the object of the present invention to provide a device for reducing the phase error of a superconducting undulator according to the preamble of claim 1, which does not have the aforementioned disadvantages and limitations.

It should be provided a device that with little effort easy to use. In particular, the phase error should be able to be reduced by means of such a device without requiring cooling, heating and renewed cooling of the superconducting undulator.

This object is solved by the characterizing features of claim 1. The subclaims describe advantageous embodiments of the invention.

The device according to the invention serves to reduce the phase error of a superconducting undulator having two rows of juxtaposed magnetic poles between which the beam is passed, with two adjacent poles in a row differing in the sign of their magnetic field. The device according to the invention has at least one closed superconducting loop which is arranged so that it encloses at least two poles in one of the two rows of the undulator. This type of arrangement according to the invention ensures that regardless of which of the two poles in one of the two rows of the undulator, which lies within a closed loop, actually has an error, the phase error occurring thereby is compensated.

In a particularly preferred embodiment, the at least one superconductive loop is arranged so that it is between the two rows of the undulator, between which the beam is performed.

In a particular embodiment, an even number of adjacent poles in each of the two rows of the undulator is enclosed with a superconducting loop.

If at least two closed superconducting loops are provided, then in a preferred embodiment, in each case two adjacent superconducting loops are arranged such that they overlap one another.

If at least two closed superconducting loops are provided, then in a further preferred embodiment, in each case two adjacent superconducting loops are arranged such that they lie against one another and are coupled to one another by magnetic fields.

In a particularly preferred embodiment, a row contains at least two, preferably a plurality of closed superconducting loops, which are arranged such that in each case two adjacent poles in one of the two rows of the undulator are provided with a superconducting loop enclosing them. With the exception of the first and last pole in the series, in this case the superconducting loops are arranged with respect to each other such that each pole in one of the two rows of the undulator is simultaneously enclosed by two adjacent superconducting loops.

The physical effect achieved with the device according to the invention can be explained as follows:

If a superconducting closed loop is applied for a period with two poles, then the current induced in the superconducting loop when the undulator is turned on will be identical to zero if the two poles, in absolute terms, have the same high field strengths.

In practice, however, an undulator is never perfect and the two poles, in absolute terms, have a different field. Therefore, a current is induced in the loop according to the known law of Lenz. However, the magnetic field of the induced current counteracts the induced field and reduces it to zero. In this way, such a loop compensates for two different poles of the undulator due to mechanical errors.

However, in practice it is not clear in advance which of the periodic poles in one of the two rows of the undulator have an error. Therefore, according to the present invention, the following preferable arrangement is proposed: A number of n ≥ 2 closed superconducting loops are superimposed in relation to each other so that two loops each cover a single pole together.

In mathematical terms, such an arrangement means for n different poles in one of the two rows of an undulator with the respective magnetic field strength (u ₁ , -u ₂ , u ₃ , -u ₄ , ..., U _n ) the following system of equations: $$\begin{array}{ccc}{\mathit{<figure-callout\; id="1"\; label="u"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">u</figure-callout>}}_{\mathit{1}}\mathit{+}{\mathit{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathit{1}}\hfill & =& x\\ \mathit{-}{\mathit{<figure-callout\; id="2"\; label="u"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">u</figure-callout>}}_{\mathit{2}}\mathit{+}{\mathit{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathit{1}}\mathit{+}{\mathit{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathit{2}}\hfill & =& -x\\ {\mathit{u}}_{\mathit{3}}\mathit{+}{\mathit{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathit{2}}\mathit{+}{\mathit{<figure-callout\; id="3"\; label="k"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathit{3}}\hfill & =& x\\ \mathit{...}& & \\ {\mathit{u}}_{\mathit{n}}\mathit{+}{\mathit{k}}_{\mathit{n}\mathit{-}\mathit{1}}\hfill & =& x\end{array}$$

Here, x denotes the new field value, k ₁ to k _n-1 are the correction values generated by the coils. Since the field through the coils was equal to zero before the coils were switched on, according to the law of Lenz, this value remains only if the new field in all partial coils is exactly identical x. Since the illustrated system of equations with n unknowns consists of n equations, it is uniquely solvable.

In this way, it can be seen that the arrangement according to the invention, which in this example comprises n additional superconducting coils which are introduced into the undulator, independently compensate for the errors.

In a particularly preferred embodiment, the at least one closed superconducting loop is applied to a substrate (foil) or introduced into a substrate (foil). This substrate (foil) is preferably located on one side of the magnetic poles located in one of the two rows.

The at least one closed superconductive loop is made of a material which preferably contains a high-temperature superconductor. On the other hand, closed superconducting loops are also used, which consist of a material containing a low-temperature superconductor.

The device according to the invention, whose loops are additionally introduced into the undulator, compensates for the phase errors of the superconducting undulator independently. Thus, the phase error can be reduced without requiring cooling, warming, and re-cooling of the superconducting undulator.

Fig. 1

Darstellung der in den beiden Reihen eines supraleitenden Undulators auftretenden mechanischen Abweichungen durch Abweichungen der Pol- oder Leiterbündelposition.

Fig. 2a

Alternierendes Magnetfeld mit einem Pol, der sich an abweichender Position (Polhöhe) befindet.

Fig. 2b

Differenz (durchgezogene Linie) zwischen idealem Undulator-Feld und Feld mit Polfehler.

Fig. 3a

Alternierendes Magnetfeld mit einem Leiterbündel, das sich an abweichender Position befindet.

Fig. 3b

Differenz (durchgezogene Linie) zwischen idealem Undulator-Feld und Feld mit Leiterbündelfehler.

Fig. 4a

Geschlossene supraleitende Schleife um eine Periode mit 2 Polen: Prinzipdarstellung mit Rechtecksfeld.

Fig. 4b

n geschlossene supraleitende Schleifen in einer der beiden Reihen: Prinzipdarstellung mit Rechtecksfeld.

Fig. 5

Darstellung eines Zwei-Perioden-Felds mit Polfehler, korrigiert mit einer Vorrichtung aus 3 geschlossenen supraleitenden Schleifen: vor (gestrichelte Linie) bzw. nach der Korrektur (durchgezogene Linie).

The invention will be explained in more detail below with reference to embodiments and figures. Hereby show:

Fig. 1

Representation of occurring in the two rows of a superconducting undulator mechanical deviations by deviations of the pole or conductor bundle position.

Fig. 2a

Alternating magnetic field with a pole that is at a different position (pole height).

Fig. 2b

Difference (solid line) between ideal undulator field and field with pole error.

Fig. 3a

Alternating magnetic field with a conductor bundle that is in a different position.

Fig. 3b

Difference (solid line) between ideal undulator field and field with fiber bundle error.

Fig. 4a

Closed superconducting loop around a period with 2 poles: schematic diagram with square field.

Fig. 4b

n Closed superconducting loops in one of the two rows: Schematic diagram with rectangular field.

Fig. 5

Representation of a two-period field with pole error, corrected with a device consisting of 3 closed superconducting loops: before (dashed line) or after correction (solid line).

The possible magnetic errors, as they occur in a real superconducting undulator, shows by way of example Fig. 1 , The undulator shown there has two coils 1, 2 , between which there is a gap 3 into which an electron beam can be introduced. In the coils 1, 2 superconducting conductor packages in the form of wire bundles 11, 12, 13, 14, 15 (upper row), 21, 22, 23, 24, 25 (lower row) are mounted. Due to errors in the height of the wire bundles 21, 22 from the superconducting conductor packages and in the height of the poles between the wire bundles 13 and 14 or 24 and 25 , the fields are different from period to period.

Fig. 2a shows an alternating magnetic field as observed with a pole located at a different position (pole height) can. This deviation leads to the in Fig. 2b shown difference (solid line) between the ideal undulator field (dashed line) and the actually observable field with pole error Fig. 2a ,

Fig. 3a shows an alternating magnetic field, as can be observed with a conductor bundle, which is located at a different position. This deviation leads to the in Fig. 3b shown difference (solid line) between the ideal undulator field (dashed line) and the actually observable field with conductor bundle error Fig. 3a ,

• u₁, u₂ die unkorrigierten Magnetfeldstärken der beiden Pole,
• w₁, w₂ die mittels der erfindungsgemäßen Vorrichtung korrigierten Magnetfeldstärken der beiden Pole und
• y₁ die geschlossene supraleitende Schleife.

In Fig. 4a schematically a closed superconducting loop used according to the invention is shown around a period with two poles as a schematic diagram with a rectangular field. Denote this

• u ₁ , u _{2 are} the uncorrected magnetic field strengths of the two poles,
• w ₁ , w ₂ the corrected by means of the inventive device magnetic field strengths of the two poles and
• y _{1 is} the closed superconducting loop.

• u₁,...u_n+₁ die n unkorrigierten Magnetfeldstärken der beiden Pole und
• y₁,...yn die n geschlossenen supraleitenden Schleifen.

In Fig. 4b n ≥ 2 closed superconducting loops used according to the invention are each shown by a period with two poles as a schematic representation with a rectangular field. Here, each two adjacent superconducting loops are arranged so that they lie in a row together and are coupled together by magnetic fields. To designate it

• u ₁ , ... u _n + ₁ the n uncorrected magnetic field strengths of the two poles and
• y ₁ , ... yn the n closed superconducting loops.

Fig. 5 shows a two-period field with pole errors corrected with a three closed superconducting loop device according to the invention. This correction leads from the magnetic field shown as a dashed line to the corrected magnetic field shown as a solid line.

Claims (8)

1. Device for reducing phase error of a superconducting undulator, having two rows (11, 12, 13, 14, 15; 21, 22, 23, 24, 25) of magnetic poles disposed next to each other, the magnetic fields of any two adjacent poles in one of the rows having different signs and the device comprising at least one closed superconducting loop (y₁,...y_n), characterised in that the least one closed superconducting loop (y₁,...y_n) is disposed such that it encompasses at least two poles in one of the two rows of the undulator.
2. Device according to claim 1, characterised in that the at least one superconducting loop (y₁,...y_n) is located between the two rows (11, 12, 13, 14, 15; 21, 22, 23, 24, 25) of the undulator.
3. Device according to claim 1 or 2, characterised in that an even number of adjacent poles from one of the two rows (11, 12, 13, 14, 15; 21, 22, 23, 24, 25) are equipped with a superconducting loop (y₁,...y_n) encompassing them.
4. Device according to any one of claims 1 to 3, characterised in that the device comprises, in one of the two rows (11, 12, 13, 14, 15; 21, 22, 23, 24, 25), at least two closed superconducting loops (y₁, y₂, ..., y_n-1, y_n), wherein at least two adjacent superconducting loops (y₁, y₂, ..., y_n-1, y_n) overlap each other.
5. Device according to any one of claims 1 to 4, characterised in that the device comprises, in one of the two rows (11, 12, 13, 14, 15; 21, 22, 23, 24, 25), at least two closed superconducting loops (y₁, y₂, ..., y_n-1, y_n), wherein at least two adjacent superconducting loops (y₁, y₂, ..., y_n-1, y_n), coupled by magnetic fields, contact one another.
6. Device according to any one of claims 1 to 5, characterised in that the device comprises, in one of the two rows (11, 12, 13, 14, 15; 21, 22, 23, 24, 25), at least two closed superconducting loops (y₁, y₂, ..., y_n-1, y_n), wherein any two adjacent poles of the undulator are equipped with a superconducting loop (y₁,,...y_n) encompassing them and, with the exception of the first and last pole in one of the two rows, the superconducting loops (y₁, y₂, ..., y_n-1, y_n) are disposed with respect to one another such that each pole in one of the two rows (11, 12, 13, 14, 15; 21, 22, 23, 24, 25) is simultaneously encompassed by two adjacent superconducting loops (y₁, y₂, ..., y_n-1, y_n) each.
7. Device according to any one of claims 1 to 6, characterised in that the at least one closed superconducting loop (y₁,...y_n) is applied onto a substrate or introduced into a substrate.
8. Device according to any one of claims 1 to 7, characterised in that the at least one closed superconducting loop (y₁,...y_n) comprises a material which contains a high-temperature superconductor.

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