Pith. sign in

REVIEW 4 major objections 6 minor 144 references

The Magnetic Toroidal Sector as A broad-band Electron-Positron Pair Spectrometer I. Lepton Trajectories

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A toroidal magnetic sector images both leptons of a pair onto field-invariant arcs, so one calibration serves every field setting.

desk verdict A plausible but under-supported design study: the toroidal pair-spectrometer concept is worth refereeing, but the central invariance claim needs proof and the efficiency claims need numbers. read the letter →

arxiv 1908.01019 v1 pith:4FTPBFGM submitted 2019-08-02 physics.ins-det

Siegbert Hagmann , Pierre-Michel Hillenbrand , Yurij Litvinov , Uwe Spillmann , Thomas Stöhlker This is my paper · ORCID
classification physics.ins-det
keywords toroidalmagneticspectrometerelectron-positronpairspectroscopyfree-freeproductionmomentumdispersioninvarianceleptontrajectorysimulationstorageringinstrumentationdetectorcalibrationcoincidencedetection
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that a toroidal magnetic sector can serve as a broad-band electron-positron pair spectrometer for free-free pair production at a relativistic heavy-ion storage ring. Its central finding is that, for a fixed detector plane, the curves traced by leptons with zero transverse momentum are geometrically invariant under changes of the magnetic field: changing B only moves a lepton of given momentum along the same arc, and the focus points on the arcs stay fixed while the momentum they represent scales with B. The same field separates electrons and positrons to opposite sides of the bend plane, so a single device can detect both members of a pair in coincidence over a nearly $4\pi$ solid angle. That would make it possible to measure threefold and partially fourfold differential cross sections of free-free pair production, which have not been measured before.

What carries the argument

The central object is the toroidal magnetic field $\vec{B} = \frac{A(i)}{R}\,\vec{e}_\varphi$ and the momentum-dispersion arcs $C_+$ and $C_-$ it imprints on a detector plane. The load-bearing mechanism is the combination of helical gyration around the field line with the $1/R$ field gradient, which makes the gyration radius smaller on the inner side of the helix than on the outer side; the resulting drift separates opposite charges perpendicular to the bend plane and creates the arcs. The paper also uses the cyclotron time-of-flight relation $T = n f^{-1} = n(2\pi\gamma m_0)/(qB)$ to identify foci $X_n$ at momenta $p_n = \beta\gamma/n$, and the Jacobian identities $d^2\sigma'/dE'\,d\Omega' = (p/p')\,d^2\sigma/dE\,d\Omega$ and $d^2\sigma'/dp'\,d\Omega' = (\gamma/\gamma')(p'^2/p^2)\,d^2\sigma/dp\,d\Omega$ to convert laboratory-frame cross sections into emitter-frame cross sections.

What would settle it

Simulate or build the real coil set and record, on the detector plane, the intercepts of monoenergetic leptons with zero initial transverse momentum at two field strengths differing by a factor of ten, for example 108.7 G and 1087 G; if the intercept loci do not reproduce the same geometric arcs and the same focus locations within the roughly 0.5 mm detector resolution, the central invariance claim fails. A cheaper check is the paper's 207Bi 975.7 keV conversion-electron mapping: over a sequence of B values, the intercept positions should collapse onto one field-independent curve, with only the momentum labels changing.

Watch

Extended reading notes

Core claim

The discovery the paper is trying to establish is an invariance property of lepton trajectories in a toroidal field $\vec{B} = \frac{A(i)}{R}\,\vec{e}_\varphi$. For leptons launched from one point with laboratory momentum along the beam (transverse momentum $p_\perp=0$), the intersections with a detector plane at toroidal angle $\varphi$ map out an electron arc $C_-$ and a positron arc $C_+$ whose geometry depends only on the toroidal radius and on $\varphi$, not on the magnetic field strength. Increasing $B$ slides each momentum value along the arc toward the midpoint; decreasing $B$ slides it outward. The same geometric invariance holds for the foci $X_n$, where leptons with momenta $\beta\gamma/n$ converge after $n$ cyclotron periods: the focal locations on the arcs are fixed, and the momentum assigned to each focus is proportional to $B$. The paper demonstrates this with three-dimensional magnetostatic field and trajectory calculations for a realistic segmented-coil configuration with field deviations of about $\pm 1\times10^{-3}$ from the ideal $1/R$ toroidal field, and it uses the invariance to propose a calibration strategy based on the electron cusp and on conversion-electron lines.

Load-bearing premise

The load-bearing premise is that the numerically computed magnetic field and trajectories for the realistic segmented-coil design match the real spectrometer closely enough that the geometric invariance of arcs and foci holds at the level of the detector's position resolution; the paper presents no experimental field measurement, mesh-convergence test, or tolerance analysis to confirm this.

Editorial extensions

If this is right

  • One detector array and one calibration procedure serve every magnetic-field setting, because the arcs and foci do not move; only the momentum scale changes.
  • A single toroidal sector can record the electron and the positron of the same pair in coincidence, because opposite charges disperse to opposite sides of the bend plane.
  • The electron-cusp location on the electron arc provides an in-situ momentum calibration tied directly to the beam velocity.
  • With 2D position-sensitive detectors placed on and around the arcs, the device can deliver 3DCS and partially 4DCS for free-free pair production.
  • The magnetic field can be tuned to slide a wanted lepton momentum window along the invariant arcs without redesigning the detector layout.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same geometric invariance should hold for any coil geometry that produces the ideal $1/R$ toroidal field; the segmented-coil result suggests the property is robust, but the $\pm 1\times10^{-3}$ field deviations put a floor on how precisely the invariance survives in a real device.
  • Because the focus momenta scale as $p_n = \beta\gamma/n$, the focus grid could act as a built-in ruler: once the geometric locations are mapped at one field value, the same detector layout covers a wide momentum range by changing $B$ alone.
  • The intermediate foci ($n>1$) offer a natural multi-plane coincidence filter: a small detector at an intermediate focus selects one low-momentum group while the main detector plane handles higher momenta, which could sharpen electron-positron coincidence measurements.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript analyzes the electron-optical properties of a toroidal magnetic sector spectrometer for coincident e+e- pair spectroscopy at the HESR storage ring. The core claim is that at a fixed detector-plane angle φ, the momentum-dispersion arcs C+ and C- traced by leptons with zero initial transverse momentum are invariant under changes of the toroidal B-field, and that the foci Xn on these arcs are geometrically invariant as well, with only the lepton momentum assigned to each location scaling with B. The paper argues that this invariance, together with the kinematic focusing of leptons from relativistic projectiles, permits a single detector layout and calibration to cover a wide range of lepton momenta and to enable 3DCS and partial 4DCS measurements. The supporting evidence is OPERA-3D trajectory calculations for a segmented-coil field that deviates from the ideal 1/R field by about ±1e-3, together with a standard Lorentz-Jacobian derivation (Eqs. 12-13) for transforming differential cross sections between laboratory and emitter frames.

Significance. The proposed geometry is conceptually attractive and, if the invariance claims were established quantitatively, would be a significant step toward kinematically complete pair spectroscopy. The Lorentz transformation results in Eqs. (12)-(13) and Appendix 2 are correct and clearly derived, and the paper is honest about several limitations, such as the restricted angular range in Sec. 6b and the deferred Hamiltonian treatment in Appendix 1. However, the central claims regarding invariant arcs and foci, as well as the high-coincidence-efficiency and near-4π acceptance, are currently supported only by example simulations without error propagation, convergence studies, or a quantitative acceptance calculation. The paper is therefore a promising design study but does not yet justify its headline claims.

major comments (4)
  1. [Sec. 6a/6d, Figs. 18 and 25] The load-bearing claim that the arcs C+ and C- and the foci Xn are exactly invariant under B-field scaling is not supported by the presented evidence. The only evidence is OPERA-3D runs on a segmented-coil field with ±1e-3 deviations from the ideal B=A/R (Sec. 5, Figs. 12-13); there is no analytic derivation for the ideal field, and Appendix 1 explicitly defers the Hamiltonian treatment to a forthcoming paper. No mesh-refinement or convergence study is presented, and no tolerance analysis translates the 1e-3 field error into uncertainties on arc and focus positions. Because the invariant-arc property is used in Secs. 6a and 6d to justify a single detector layout and calibration for all field settings, either an analytic proof or a quantified numerical error analysis is needed.
  2. [Abstract and Sec. 7] The abstract and summary claim "very high efficiencies for coincident e+e- pair spectroscopy" and "near 4π solid angle," but the manuscript contains no quantitative acceptance or efficiency calculation. Section 6 shows example trajectories and allowed regions (e.g., Figs. 23a,b), but never defines the detection acceptance as a function of momentum and emission angle for either lepton, nor the coincidence efficiency. Because the high coincidence efficiency is the key motivation for the design, this omission prevents the reader from assessing whether the spectrometer can meet its stated purpose.
  3. [Sec. 6b, Eq. (9)] The focus condition is based on a time-of-flight argument using a well-defined cyclotron frequency, but the paper itself notes that for large gyroradii the trajectories sample regions where B deviates from 1/R, producing azimuth-dependent interceptions instead of clean foci. No quantitative criterion is given for the maximum gyroradius or emission angle for which Eq. (9) remains valid, and the analysis is explicitly restricted to θ_lab ≤ 20° in Sec. 6b. This restriction is inconsistent with the near-4π acceptance claim and leaves the focal-invariance property unquantified for the full angular range.
  4. [Sec. 6c, Figs. 21-22] The calibration procedure using cusp electrons and 207Bi conversion lines is described only for specific example settings, such as 108.7 G in Figs. 21-22, and its generalization to arbitrary fields is stated to rely on the invariant-arc property. Without the quantitative support requested above, the calibration scheme, while plausible, is not demonstrated at the level expected for a design study; the authors should show at least a few more field settings and quantify the residuals between the planned and fitted calibration curves.
minor comments (6)
  1. [Fig. 12 caption] The caption refers to "the coils shown in fig. 10," but the coil assembly is shown in Fig. 11; the cross-reference should be corrected.
  2. [Eq. (5a)] Equation (5a) contains an unbalanced parenthesis in the square root, and the denominator is ambiguous; it should be typeset with clear parentheses for the two terms in the denominator.
  3. [Table of contents] The table of contents lists Section 3 as "The high energy storage ring HESR," but the main text appears to skip a Section 2 heading; check the section numbering throughout the manuscript.
  4. [Sec. 5] The phrase "see also Appenix 1" contains a typo; it should read "Appendix 1."
  5. [Sec. 6c] The energy units are used inconsistently, with both "481.7 KeV" and "975.7 keV" appearing in nearby text; a single convention should be adopted.
  6. [References] A few references are incomplete, for example ref. 50 ("Rev. 129 1619" lacks the journal name); the reference list should be checked for completeness and consistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the invariant-arc and focus claims are numerical simulation outputs with external calibration, not fitted inputs renamed as predictions.

full rationale

The paper's central claims—geometric invariance of the momentum arcs C+ and C- and of the foci Xn under variation of the toroidal magnetic field—are presented as outputs of OPERA-3D magnetostatic field calculations and trajectory integrations (Secs. 5 and 6), not as algebraic consequences of a fitted or self-cited model. No parameter is fitted to a subset of trajectory data and then 'predicted' as a closely related quantity. Calibration uses the cusp electron energy E/1822.8878 and 207Bi conversion-electron lines as external benchmarks (Sec. 6c), and the Lorentz-frame Jacobian results in Eqs. (12)-(13) are derived explicitly in Appendix 2 from standard Lorentz transformations with attribution to Panofsky/Dedrick/Hagedorn rather than to the present authors. Self-citations to Ref. [124] for cusp properties and to Refs. [57,60] for HESR parameters are contextual and do not carry the load-bearing invariance argument. The main weakness—that the invariance is established by numerical simulation for a specific segmented-coil field with ΔB/B≈1e-3 and without a convergence or tolerance study—is a verification/completeness concern, not circularity, because the simulation inputs do not encode the claimed invariant arcs or foci as outputs.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claims rest on standard relativistic kinematics and on commercial magnetostatic simulations of a not-yet-built coil. No parameters are fitted to data. The main unverified inputs are the OPERA-3D field model, its uniformity tolerance, and the completeness of the coil geometry description.

assumptions (6)
  • domain assumption Ideal toroidal field B = A/R with a purely meridional coil current
    Eq. 7 and Sect. 5; this field is the basis for the charge-separation drift and for the arc/foci claims. The real coil is segmented with field deviations quoted as about +/-1e-3.
  • domain assumption OPERA-3D TOSCA field and trajectory calculations are accurate
    Sect. 5 and 6; all arcs, foci, and dispersion plots come from OPERA-3D without meshing or error convergence details.
  • domain assumption The +/-1e-3 field uniformity is sufficient for the invariant-arc property to hold
    Sect. 5, Figs. 12-13; no quantitative link from field error to trajectory intercept error is established.
  • standard math The Lorentz transformation Jacobian relations in Eqs. 12 and 13 are standard and correctly evaluated
    Appendix 2; these are textbook results attributed to Panofsky, Hagedorn, and Dedrick, and are used to transform measured cross sections into the emitter frame.
  • domain assumption The two leptons of a pair transform independently, so the Jacobian factorizes
    Sect. 6e; this is true for the pure Lorentz transformation of one lepton given its lab variables, but assumes no additional coupling from detector acceptance or field effects.
  • domain assumption Beam compensation steerers will restore the stored coasting beam
    Sect. 3 and 5; the paper notes that corresponding compensation calculations are in progress, so in-ring applicability is not yet demonstrated.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Magnetic Toroidal Sector as A broad-band Electron-Positron Pair Spectrometer I. Lepton Trajectories." pith.science (2026). https://pith.science/paper/4FTPBFGM

@misc{pith2026190801019,
  author       = {Pith},
  title        = {Pith review of: The Magnetic Toroidal Sector as A broad-band Electron-Positron Pair Spectrometer I. Lepton Trajectories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4FTPBFGM}},
  note         = {Machine review of arXiv:1908.01019}
}
abstract

We report an analysis of electron-optical properties of a toroidal magnetic sector spectrometer and examine parameters for its implementation in a relativistic heavy-ion storage ring like HESR. For studies of free-free pair production in heavy-ion atom collisions this spectrometer exhibits very high efficiencies for coincident $e^+e^-$ pair spectroscopy over a wide range of momenta of emitted lepton pairs. The high coincidence efficiency of the spectrometer is the key for stringent tests of theoretical predictions for the coincident positron- and electron- emission characteristics and for the phase space correlation of lepton vector momenta in free-free pair production.

Figures

Figures reproduced from arXiv: 1908.01019 by the authors.

Figure 4
Figure 4. in Moon [PITH_FULL_IMAGE:figures/full_fig_p062_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

144 extracted references · 80 canonical work pages

  1. [1]

    Ruffini et al

    R. Ruffini et al. Physics Report 487 1-140 (2010)

    2010

  2. [2]

    Eichler, W

    J. Eichler, W. E. Meyerhof, Relativist. Atomic Coll., Academic Press (1995)

    1995

  3. [3]

    Voitkiv, J

    A. Voitkiv, J. Ullrich, Relativistic Collisions, Springer Series AOPP, Vol. 49 (2008)

    2008

  4. [4]

    Bethe et al., Proc Roy Soc A146 83-112 (1934)

    H. Bethe et al., Proc Roy Soc A146 83-112 (1934)

    1934

  5. [5]

    H. A. Bethe et al., Phys. Rev. 93, 768 (1954)

    1954

  6. [6]

    allowed regions

    Invariants and other serendipitous features of lepton trajectories in a toroidal B-field Toroidal magnetic spectrometers permit to simultan eously investigate e + and e - continua from free-free pair production emitted in heavy ion atom collisions due to the separation of leptons of opposite charge perpendicular to the centre plane of the toroid. In the f...

    work page arXiv 2000

  7. [7]

    Due to considerable computational requirements theory shows only partial DDCS, but no fully 4DCS 𝑑4𝜎 𝑑𝐸𝑒+𝑑𝛺𝑒+𝑑𝐸𝑒−𝑑𝛺𝑒−

    Summary Free-free pair production cross sections in near relativistic ion -atom collisions are predicted to produce lepton pairs over a wide range of momenta and relative emission directions- contrary to photon induced case . Due to considerable computational requirements theory shows only partial DDCS, but no fully 4DCS 𝑑4𝜎 𝑑𝐸𝑒+𝑑𝛺𝑒+𝑑𝐸𝑒−𝑑𝛺𝑒−. We present a...

    2020

  8. [8]

    Sauter, Ann

    F. Sauter, Ann. Physik 412, 404 (1934)

    1934

Show all 144 references
  1. [9]

    Sommerfeld, Ann Physik 403, 257 (1931)

    A. Sommerfeld, Ann Physik 403, 257 (1931)

    1931

  2. [10]

    Oppenheimer et al., Phys

    J. Oppenheimer et al., Phys. Rev. 44, 53 (1933)

    1933

  3. [11]

    Heitler, Z

    W. Heitler, Z. f. Phys. 84, 145 (1933)

    1933

  4. [12]

    L. D. Landau, E. M. Lifshitz, Phys. Z. Sowjet Union 6, 244 (1934)

    1934

  5. [13]

    Racah, Il Nuovo Cim 11 477-481 (1934) pair prod

    G. Racah, Il Nuovo Cim 11 477-481 (1934) pair prod

    1934

  6. [14]

    Racah, Nuovo Cimento 14 (1937) 93

    G. Racah, Nuovo Cimento 14 (1937) 93

    1937

  7. [15]

    Baur et al

    G. Baur et al. Phys. Rep. 453 1-27 (2007)

    2007

  8. [16]

    Baur et al

    G. Baur et al. Phys. Rep. 364 359 (2002)

    2002

  9. [17]

    Baur et al

    G. Baur et al. J. Phys G24, 1657 (1998) pair

    1998

  10. [18]

    Hencken et al

    K. Hencken et al. Phys. Rev. A59 841 (1999)

    1999

  11. [19]

    Segev et al

    B. Segev et al. Phys. Rev. C59 2753 (1999)

    1999

  12. [20]

    Ionescu, Habilitationsschrift, Freie Universität Berlin (1997)

    D. Ionescu, Habilitationsschrift, Freie Universität Berlin (1997)

    1997

  13. [21]

    C. A. Bertulani et al. Phys. Rep. 163 299 (1988)

    1988

  14. [22]

    C. A. Bertulani et al., Ann. Rev. Nuc. Part. Sci. 55, 271 (2005) UPC

    2005

  15. [23]

    Baltz et al

    A. Baltz et al. Phys. Rep. 458 1 (2008) UPC

    2008

  16. [24]

    Baltz et al

    A. Baltz et al. Phys. Rev. A47 3444 (1993), Phys. Rev. A50 4842 (1994) 60 60

    1993

  17. [25]

    Strayer et al

    M. Strayer et al. Phys. Rev. A41 1399 (1990),

    1990

  18. [26]

    H. J. Bhabha, Proc. Roy Soc A152, 559 (1935)

    1935

  19. [27]

    H. J. Bhabha, Proc. Cambridge Phil. Soc. 31, 394 (1935)

    1935

  20. [28]

    Becker et al

    U. Becker et al. J. Phys. B19, 1347 (1986) pair

    1986

  21. [29]

    Becker et al

    U. Becker et al. J Phys. B20, 2075 and 6563 (1987) bound free pair

    1987

  22. [30]

    Tenzer, Dissertation, Univ

    R.W. Tenzer, Dissertation, Univ. Giessen (1999)

    1999

  23. [31]

    R. W. Tenzer et al. Eur. Phys. J. D 11 347-353 (2000)

    2000

  24. [32]

    Gail et al

    M. Gail et al. 2003 J. Phys. B: At. Mol. Opt. Phys. 36 1397

    2003

  25. [33]

    Gail et al

    M. Gail et al. Phys. Scr. T92 317-318 (2001) non-pert-th

    2001

  26. [34]

    Agger Dissertation Univ Aarhus (1996) ph-induced pair

    C. Agger Dissertation Univ Aarhus (1996) ph-induced pair

    1996

  27. [35]

    Artemyev et al

    A. Artemyev et al. Phys. Rev. A79 032713 (2009) neg cont

    2009

  28. [36]

    Belkacem et al

    A. Belkacem et al. Phys. Rev. A56 2806 (1997)

    1997

  29. [37]

    Ionescu et al

    D. Ionescu et al. Phys. Rev. A54 4960-4967 (1996) bound pair,

    1996

  30. [38]

    Ionescu et al

    D. Ionescu et al. Phys. Rev. A48 1176 (1993) free-free

    1993

  31. [39]

    Rumrich et al

    K. Rumrich et al. Phys. Rev. Lett. 66 2613 (1991) Phys. Rev. A47 215 (1993)

    1991

  32. [40]

    Thiel et al

    J. Thiel et al. Phys. Rev. A46 2607 (1992)

    1992

  33. [41]

    Vane et al Phys

    C. Vane et al Phys. Rev. A56 3682-3686 (1997)

    1997

  34. [42]

    Belkacem et al

    A. Belkacem et al. Phys. Rev. A58 1253-1255 (1998)

    1998

  35. [43]

    Meier et al

    H. Meier et al. Phys. Rev. A63 032713 (2001) bound-free basel

    2001

  36. [44]

    Lee et al et al

    R. Lee et al et al. Phys. Rev. A63 062712 (2001) bound-pair theory 42a. D. Condren 2007 J. Phys.: Conf. Ser. 58 315 pair 2 center

    2001

  37. [45]

    O.Busic et al . Phys. Rev. A70 062707 (2004) bound pair th Scheid

    2004

  38. [46]

    Najjari et al

    B. Najjari et al. Phys. Rev. A80 012701 (2009) neg cont capt

    2009

  39. [47]

    Baltz Phys

    A. Baltz Phys. Rev. C74 054903 (2006) free pair th

    2006

  40. [48]

    Baltz et al

    A. Baltz et al. Phys. Rep. 458 1-171 (2008) UPc-cern-pair

    2008

  41. [49]

    Olsson et al

    H. Olsson et al. Phys. Rev. 114 887-904 (1959) enBS-pair

    1959

  42. [50]

    Olsson et al

    H. Olsson et al. Phys. Rev. 106 27 (1957) enBS-pair

    1957

  43. [51]

    Pratt Phys

    R. Pratt Phys. Rev. 117 1017 (1960) enBS-pair 49a. R. Pratt Phys. Rev. 119 1619 (1961) enBS-pair

    1960

  44. [52]

    Jabbur et al

    R. Jabbur et al. Rev. 129 1619 (1961) enBS-pair

    1961

  45. [53]

    Fano Phys

    U. Fano Phys. Rev. 116 1156-1158 (1963) enbs-pair ang distr 61 61

    1963

  46. [54]

    Meier et al Eu

    H. Meier et al Eu. Phys. J. C2 741-746 (1998) pair enBS

    1998

  47. [55]

    Lee et al

    R. Lee et al. Phys. Rev. A65 022102 (2002) UPC

    2002

  48. [56]

    Claytor et al

    N. Claytor et al. Phys. Rev. A55 R842 (1997) e-capture/loss

    1997

  49. [57]

    Bruce et al., Phys

    R. Bruce et al., Phys. Rev.ST Accel Beams 11, 071002(2009)

    2009

  50. [58]

    Anholt et al

    R. Anholt et al. Adv. At. Mol. Phys. 22, 315 (1986) pair-lumin-accel

    1986

  51. [59]

    Stoehlker et al

    T. Stoehlker et al. SPARC@HESR , A feasibility study , Darmstadt (2012) https://www.gsi.de/fileadmin/SPARC/documents/SPARC@HESR_FS_V26.pdf

    2012

  52. [60]

    Henning et al

    W. Henning et al. (ed) FAIR, CDR , http://www.gsi.de/GSI-future/cdr 2001

    2001

  53. [61]

    Maier et al

    R. Maier et al. HESR TDR V3.1.2 Darmstadt (2008)

    2008

  54. [62]

    Anjelkovic et al

    Z. Anjelkovic et al. Technical Design Report SPARC@HESR: Instrumentation https://www.gsi.de/work/forschung/appamml/atomphysik/ap_und_fair/sparc/dokumen te.htm

  55. [63]

    Popov JETP 65, 35 (1973)

    V. Popov JETP 65, 35 (1973)

    1973

  56. [64]

    Gerstein et al., Sov

    R. Gerstein et al., Sov. J. Exp Theor. Phys. 30, 358 (1969)

    1969

  57. [65]

    Gerstein et al., Lettere al Nuovo Cimen

    R. Gerstein et al., Lettere al Nuovo Cimen. 1,835 (1969)

    1969

  58. [66]

    Reinhardt et al

    J. Reinhardt et al. Rep. Prog. Phys. 40,219 (1977)

    1977

  59. [67]

    Greiner et al

    W. Greiner et al. QED of Strong Fields Oxford Univ. Press, Oxford (1995)

    1995

  60. [68]

    Graf et al

    O. Graf et al. Phys. Rev. Lett 61 2831-2834 (1988) pair ang corr

    1988

  61. [69]

    Tupitsyn et al., Phys

    I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)

    2010

  62. [70]

    Artemyev et al

    A. Artemyev et al. Phys. Rev. A 79, 032713 (2009); A. Artemyev et al. Phys. Rev. A 67, 052711 (2003); Neg cont DR

    2009

  63. [71]

    Najjari et al

    B. Najjari et al. Phys. Rev. A 80, 012701 (2009)

    2009

  64. [72]

    Y Yerokhin et al. Phys. Rev. A 92, 042708 (2015)neg cont DR

    2015

  65. [73]

    Hagedorn Relativistic Kinematics, W

    R. Hagedorn Relativistic Kinematics, W. A. Benjamin, NY, (1963)

    1963

  66. [74]

    Blaton Mat.-Fys

    J. Blaton Mat.-Fys. Medd 24 1-31 (1950) kinematik

    1950

  67. [75]

    Goldanski et al

    V. Goldanski et al. Kinematic methods in Hgh Energy Physics (1989)

    1989

  68. [76]

    Trower Kinematics of particles UCRL-2426 U

    W. Trower Kinematics of particles UCRL-2426 U. of California (1965)

    1965

  69. [77]

    Herath Banda et al

    M.A. Herath Banda et al. , Phys. Rev. A 33, 861 (1986)

    1986

  70. [78]

    Kienle et al

    P. Kienle et al. in Proc. Conf. NATO Adv. Study Inst. on QED of Strong Fields, Lahnstein, NATO Adv. Study Inst. Series B80 (1983)

    1983

  71. [79]

    Backe et al

    H. Backe et al. Phys. Rev. Lett 40 1443 (1978)

    1978

  72. [80]

    Krieg et al

    R. Krieg et al. Nuc. Inst. Meth Phys B9 762-766 (1985) spectrom 62 62

    1985

  73. [81]

    E.Kankeleit et al. Nuc. Inst. Meth Phys A234 81-90 (1985)

    1985

  74. [82]

    Ter-Akopian et al

    G. Ter-Akopian et al. Int Journal Mod Phys.E24 1550016 (2015) positron spec

    2015

  75. [83]

    OPERA-3D User Guide, Vector Fields Limited, 24 Bankside, Kidington, Oxford OX5 1JE, UK

  76. [84]

    Wang et al

    X. Wang et al. Meas. Sci. Technol. 18 161–166 (2007)

    2007

  77. [85]

    Wollnik, Optics of charged particles, (1987) Academic Press, N.Y

    H. Wollnik, Optics of charged particles, (1987) Academic Press, N.Y

    1987

  78. [86]

    Kawachi et al

    A. Kawachi et al. Nuc. Inst. Meth Phys A416 253-262 (1998) tori

    1998

  79. [87]

    Wüstling et al

    S. Wüstling et al. Nuc. Inst. Meth Phys A568 382-390 (2006) 64pinSili

    2006

  80. [88]

    Wüstling et al

    S. Wüstling et al. Nuc. Inst. Meth Phys A624 295-302 (2010) 64pin

    2010

  81. [89]

    Efremov et al

    A. Efremov et al. Nuc. Inst. Meth Phys A585 182-200 (2008) panda-solen

    2008

  82. [90]

    Ullrich, V

    J. Ullrich, V. Shevelko, Many-Particle Quantum Dynamics in Atomic and Molecular Fragmentation, Springer Series AOPP, Vol. 35 (2003)

    2003

  83. [91]

    Deco et al

    G. Deco et al. 1989 J. Phys. B: At. Mol. Opt. Phys. 22 1043

    1989

  84. [92]

    Picone Nuc

    J. Picone Nuc. Inst. Meth Phys 105 377-379 (1972) beta ICspec;UCLEAR

    1972

  85. [93]

    Dörscher, Dissertation Univ

    S. Dörscher, Dissertation Univ. Hamburg (2013) Yb-Mot

    2013

  86. [94]

    Robin et al Nuc

    D. Robin et al Nuc. Inst. Meth Phys A659 484-493 (2011) toroid inclined coils

    2011

  87. [95]

    Petridis et al

    N. Petridis et al. Technical Report: Design of the TARGET@HESR (2013)

    2013

  88. [96]

    Abdullaev and K

    S. Abdullaev and K. Finken, Phys Plasma 9, 4193 (2002)

    2002

  89. [97]

    Abdullaev, Lecture notes in physics 691, Berlin Springer (2006)

    S. Abdullaev, Lecture notes in physics 691, Berlin Springer (2006)

    2006

  90. [98]

    Abdullaev, Springer Series on Atomic, Optical and Plasma Physics 78,1 Berlin, Springer (2014)

    S. Abdullaev, Springer Series on Atomic, Optical and Plasma Physics 78,1 Berlin, Springer (2014)

    2014

  91. [99]

    P. Moon, D. Spencer, Field theory handbook, 1961 Springer Heidelberg Figure 4.04 in Moon-Spencer depicting the coordinate surfaces contains an error in the coordinate-direction of : the radius of the spheroid decreases with increasing 

    1961

  92. [100]

    Carter et al., Quart

    G. Carter et al., Quart. J. of Mechanics and Appl. Math 18, 87-106(1965) 99a. H. Haas, Archiv. f. Elektrotechnik 58 (1976) 197ff Springer Berlin 99b. A.H. Boozer, Physics of Fluids 25, 520 (1982) toroidal coord

    1965

  93. [101]

    Schenkel et al., Annalen d

    G. Schenkel et al., Annalen d. Physik 426 541 (1939) Toroid

    1939

  94. [102]

    Schenkel, „Über das Vektorpotential und elektrische Feld stromumflossener Toroide“, Dissertation, Techn

    G. Schenkel, „Über das Vektorpotential und elektrische Feld stromumflossener Toroide“, Dissertation, Techn. Hochschule Hannover 1938

    1938

  95. [103]

    Hübschmann, „Die Ringfunktion und ihre Anwendung auf die elektrostatischen Probleme des Ringes“ ,Dissertation Univ

    H. Hübschmann, „Die Ringfunktion und ihre Anwendung auf die elektrostatischen Probleme des Ringes“ ,Dissertation Univ. Leipzig (1890)

  96. [104]

    https://en.wikipedia.org/wiki/Circles_of_Apollonius

  97. [105]

    Jahnke et al

    T. Jahnke et al. J. Electron Spectroscopy, Related Phenomena 141,229(2004)

    2004

  98. [106]

    Alfvén, Ark

    H. Alfvén, Ark. Mat. Astron. Fys. 27A-22, 1 (1940)

    1940

  99. [107]

    H. E. Mynick, Physics of Fluids 23, 1888 (1980) guiding Hamiltonian 63 63

    1980

  100. [108]

    H. D. Littlejohn, The Physics of Fluids 24, 1730 (1981) guide Hamiltonian

    1981

  101. [109]

    Weitzner, Physics of Fluids 24, 2280 (1981), axisymm field

    H. Weitzner, Physics of Fluids 24, 2280 (1981), axisymm field

    1981

  102. [110]

    R. B. White et al., Physics of Fluids 25, 575 (1982) drift Hamiltonian

    1982

  103. [111]

    Boozer, Physics of Fluids 27, 2441 (1984); drift Hamiltonian

    A. Boozer, Physics of Fluids 27, 2441 (1984); drift Hamiltonian

    1984

  104. [112]

    White et

    R.B. White et. al. Physics of Fluids 27, 2455 (1984) drift Hamilton

    1984

  105. [113]

    J. D. Meiss et al., Physics of Fluids B 2, 2563 (1990); guiding center

    1990

  106. [114]

    Yao et al., Physics of Fluids B 5, 3852 (1993); guiding center-toroid

    Q. Yao et al., Physics of Fluids B 5, 3852 (1993); guiding center-toroid

    1993

  107. [115]

    Zenitani et al., Physics of Plasmas 23, 102102 (2016); guiding in plasma

    S. Zenitani et al., Physics of Plasmas 23, 102102 (2016); guiding in plasma

    2016

  108. [116]

    Yao et al., Physics of Fluids B 4, 2429 (1992); guiding center-toroid

    Q. Yao et al., Physics of Fluids B 4, 2429 (1992); guiding center-toroid

    1992

  109. [117]

    J. M. Greene et al., The Physics of Fluids 4, 875 (1961) cylind-toroid-perturb

    1961

  110. [118]

    Salat, Z

    A. Salat, Z. f. Naturforschung 40a, 959 (1985)

    1985

  111. [119]

    Cary et al

    J. Cary et al. Rev. Mod. Phys. 81, 693 (2009)

    2009

  112. [120]

    Thomas et al

    E. Thomas et al. Comp. Phys. Comm. 100, 31 (1997)

    1997

  113. [121]

    Cohl et al

    H. Cohl et al. Phys. Rev. A64, 052509 (2001)

    2001

  114. [122]

    Cohl et al

    H. Cohl et al. Astrophys. J. 527, 86 (1999)

    1999

  115. [123]

    Cohl et al

    H. Cohl et al. Astron. Nachr. 321 363 (2000)

    2000

  116. [124]

    Boozer, Princeton Plasma Phys

    A. Boozer, Princeton Plasma Phys. Rep. PPPL-1989 and PPPL-2094 (1984)

    1984

  117. [125]

    P. M. Hillenbrand et al. Phys. Rev. A90, 042713 (2014), A90, 022707 (2014), A91, 022705 (2015)

    2014

  118. [126]

    http://mathworld.wolfram.com/ToroidalFunction.html

  119. [127]

    Abramowitz, and I

    M. Abramowitz, and I. Ste gun, Handbook of Math. Function. , 9th printing, NY, Dover, p336, 1972

    1972

  120. [128]

    NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/ Sect 14.19 Toroidal and Ringfunctions

  121. [129]

    http://people.math.sfu.ca/~cbm/aands/ corrected version of Abramowitz-Stegun, Handbook of Math Functions; Sect 8.11 Toroidal Functions

  122. [130]

    Bonheure et al

    G. Bonheure et al. Czech. J. Phys. 56 B61 (2006)

    2006

  123. [131]

    Mukhovatov et al

    V. Mukhovatov et al. Nucl. Fusion 11, 605 (1971)

    1971

  124. [132]

    J. Cl. Maxwell, A treatise on electricity and magnetism II, 2nd ed (1881)

  125. [133]

    Dedrick, Rev

    K. Dedrick, Rev. Mod. Phys. 34 429 (1962) and K. Dedrick, Stanford University,Report. M-226(1960)

    1962

  126. [134]

    N. J. Carron, Am J. Phys 63, 717(1965) toroid

    1965

  127. [135]

    Essen et al

    H. Essen et al. Progress In Electromagnetics Research B. 46 357 (2013)

    2013

  128. [136]

    Bhadra, Review of Scientific Instruments 39 1536 1968

    D. Bhadra, Review of Scientific Instruments 39 1536 1968

    1968

  129. [137]

    Brouwer et al

    L. Brouwer et al. Proc. PAC2013 WEPBA12 p 907(2013) scal mag. Potential

    2013

  130. [138]

    Wollnik, Optics of Charged Particles, Academic Press, Orlando (1987)

    H. Wollnik, Optics of Charged Particles, Academic Press, Orlando (1987)

    1987

  131. [139]

    van Milligen et al

    B. van Milligen et al. Computer Physics Communications 81, 74 (1994) 64 64

    1994

  132. [140]

    Heine, Handbuch der Kugelfunktionen, 2nd ed

    E. Heine, Handbuch der Kugelfunktionen, 2nd ed. Berlin 1881

  133. [141]

    Stern, GSFC-NASA Report X-641-71-373, (1971) Greenbelt, Md, USA

    D. Stern, GSFC-NASA Report X-641-71-373, (1971) Greenbelt, Md, USA

    1971

  134. [142]

    A. A. Mirin et al. UCRL-52069 Report, Berkeley (1976)

    1976

  135. [143]

    Hagedorn, Relativistic Kinematics, Lect

    R. Hagedorn, Relativistic Kinematics, Lect. Notes in Physics, J.D. Jackson. ed., W. Benjamin Inc, New York (1963)

    1963

  136. [144]

    T: Schlomka , Ztschft f. techn. Physik 16 480 (1935)

    1935

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.