Hybrid Helical Microundulator

Updated 10 July 2026

Hybrid helical microundulator is a short-period undulator that uses helically arranged rare-earth and steel elements to redirect magnetic flux and achieve near-ideal on-axis fields.
It combines pre-magnetized NdFeB helices with soft-magnetic steel helices to deliver an on-axis field of approximately 1.5 T while virtually canceling external stray fields.
Numerical optimization and experimental validation confirm its compact design enhances FEL and XFEL performance through improved radiation efficiency and precise field quality.

A hybrid helical microundulator is a very short-period helical undulator in which the magnetic structure is formed by helically shaped elements and, in the prototype demonstrated for compact FEL and XFEL use, by a hybrid combination of two oppositely longitudinally pre-magnetized rare-earth helices and two pre-unmagnetized steel helices. In the experimentally demonstrated implementation, the period is $d=6$ mm, the bore is $1$ mm, the active length is $L=50$ mm over eight periods, and the inferred on-axis field reaches about $1.5$ T with “virtually zero field outside,” making the device a compact high-field alternative to short-period planar permanent-magnet microundulators (Magory et al., 7 Sep 2025).

1. Definition and design scope

In the usage established for the 2025 prototype study, a helical microundulator is a short-period undulator whose magnetic structure is formed by helical permanent-magnet elements rather than by conventional multi-block planar Halbach arrays. The hybrid helical microundulator is the more important of the two demonstrated variants: it consists of two oppositely longitudinally pre-magnetized rare-earth helices alternating with two pre-unmagnetized high-permeability steel helices, all arranged around a $1$ mm bore for beam transport (Magory et al., 7 Sep 2025).

The defining purpose of the hybridization is not tunability in the APPLE sense, but flux redirection. A fully “ideal” Halbach-type helical undulator would require both longitudinally and radially magnetized helices. Because uniformly radially magnetized helices are regarded as difficult to realize in practice, the hybrid architecture replaces those difficult radially magnetized helices by soft-magnetic steel helices. The steel inserts act as flux concentrators and redirectors, so that the field near the axis approaches that of an ideal helical Halbach structure while the external field is nearly canceled (Magory et al., 7 Sep 2025).

This architecture is distinct from two related but different usages of hybridity in the undulator literature. First, an earlier NdFeB helical-undulator paper proposed, but did not experimentally realize, a four-helix hybrid consisting of two longitudinally premagnetized rare-earth helices plus two initially non-premagnetized high-permeability helices made of steel or permendur-vanadium (Balal et al., 1 Aug 2025). Second, in FEL beamline design, “hybrid planar–helical” can denote a system in which an upstream planar SASE undulator creates microbunching and a downstream APPLE II helical radiator converts that preserved bunching into circularly polarized output; this is a hybrid source configuration rather than a hybrid magnetic microundulator structure (Geloni et al., 2011).

2. Magnetic architecture and field formation

The non-hybrid reference device uses two identical NdFeB helices, oppositely magnetized in the longitudinal direction and shifted by half a period. In that configuration, the helices are assembled by screwing one into the other with a half-period phase shift. The hybrid device uses four interleaved helices over one period: two NdFeB helices with opposite axial premagnetization and two initially unmagnetized steel helices. In the final prototype, the period is $6$ mm, the length is $50$ mm, the bore diameter is $1$ mm, the NdFeB outer radius is $R_2=10$ mm, the steel outer radius is $R_{2s}=4$ mm, and the optimized longitudinal thicknesses are $1$0 mm for the NdFeB helices and $1$1 mm for the steel helices, corresponding to $1$2 and $1$3 (Magory et al., 7 Sep 2025).

For a single infinite axially magnetized helix, the reported on-axis field is

$1$4

with $1$5, $1$6, $1$7, and $1$8 the first-order MacDonald function. The printed vector form repeats $1$9 in both transverse components, but the intended meaning is a transverse helical field. Two such helices with opposite magnetization and half-period shift double the on-axis field (Magory et al., 7 Sep 2025).

For the ideal helical Halbach-type reference used to guide the hybrid design, the reported field is

$L=50$ 0

Here $L=50$ 1 is the derivative of the first-order MacDonald function. The hybrid geometry is chosen so that the steel helices redistribute the flux from the longitudinally magnetized rare-earth helices into a near-axis field “very close” to this ideal helical Halbach structure (Magory et al., 7 Sep 2025).

Numerical optimization in CST Microwave Studio established two relevant benchmarks. If equal longitudinal thicknesses $L=50$ 2 are used, the on-axis field is only about $L=50$ 3 smaller than in the ideal infinite helical Halbach undulator. Further optimization to $L=50$ 4 and $L=50$ 5 allows the hybrid structure to reach the same on-axis field as the ideal helical Halbach reference, while also making the rare-earth helices wider and mechanically more robust (Magory et al., 7 Sep 2025).

3. Fabrication, premagnetization, and metrology

A central feature of the hybrid helical microundulator is monolithic fabrication. The helices were not assembled from many small blocks; each was machined from a single solid cylinder. First, a $L=50$ 6 mm diameter axial bore was drilled by EDM using a brass electrode, chosen over mechanical drilling because NdFeB is brittle and prone to cracking. The helical grooves were then cut by Wire Electrical Discharge Machining with a $L=50$ 7 mm brass wire while coordinating cylinder rotation with linear wire motion to produce a double-helix pattern. WEDM was performed in dielectric oil, and for NdFeB the reported machining parameters were pulse current $L=50$ 8 A, pulse duration $L=50$ 9–$1.5$0s, wire tension $1.5$1 N, and feed rate $1.5$2 m/min; for the hybrid prototype the longitudinal cutting speed was about $1.5$3m/min (Magory et al., 7 Sep 2025).

After machining, the NdFeB helices were magnetized to saturation in the axial direction using a pulsed solenoid producing about $1.5$4–$1.5$5 T for several milliseconds. In the hybrid assembly, the steel helices remained pre-unmagnetized before installation. The final device was assembled by alternating the two oppositely premagnetized NdFeB helices with the two steel helices, with aluminum spacers used during testing and with explicit care to avoid mechanical damage to the premagnetized rare-earth helices during assembly (Magory et al., 7 Sep 2025).

The $1.5$6 mm bore made direct field metrology nontrivial. For the simple two-helices NdFeB device, direct on-axis measurement was considered too difficult, so the external field was measured at a minimum sensor distance corresponding to $1.5$7 mm from the axis with a Hall sensor in a Senis 3MTS USB handheld Tesla meter. Agreement between the measured external field components and CST validated the inferred on-axis field. For the hybrid study, where the assembled device has almost no external field, a compact 3D Hall probe was inserted perpendicular to the axis into a single rotating helix from the outer side and translated along $1.5$8 while the helix rotated synchronously according to

$1.5$9

Measurements at $1$0 mm and $1$1 mm from the axis showed very good agreement with CST. Residual discrepancies of several percent were attributed to slight magnetization nonuniformity, WEDM inaccuracy, and especially sensor-positioning difficulty inside the rotating helical geometry (Magory et al., 7 Sep 2025).

The 2025 NdFeB prototype paper established the immediate fabrication precedent for this route. There, two mating helices were produced simultaneously from a non-magnetized NdFeB cylinder by a thin spiral WEDM cut, then longitudinally magnetized in a pulsed solenoid using several $1$2 ms pulses with field greater than $1$3 T. That study experimentally demonstrated a $1$4 mm-period, $1$5 mm-aperture two-helix device with $1$6 T on axis and $1$7 close to unity, while identifying the same monolithic-helical machining strategy as a path toward short-period helical micro-undulators (Balal et al., 1 Aug 2025).

4. Magnetic performance and field-quality characteristics

The experimentally demonstrated performance separates clearly into a simpler all-permanent-magnet device and the hybrid device. The two-NdFeB-helices prototype produces an on-axis transverse field exceeding $1$8 T. Equation-based estimates for an infinite device gave $1$9–$6$0 T, while CST for the actual $6$1 mm structure gave $6$2–$6$3 T. The hybrid device increases the inferred on-axis field to about $6$4 T with an estimated accuracy of about $6$5, corresponding to an improvement by roughly a factor of $6$6 relative to the all-permanent-magnet double-helix prototype (Magory et al., 7 Sep 2025).

Field topology is as important as field amplitude. The simple two-helix device has a substantial external stray field, whereas the assembled hybrid device has “virtually zero field outside.” This near-cancellation is a direct signature of the intended near-Halbach flux closure and is one of the main distinctions between the hybrid microundulator and the simpler two-helix arrangement (Magory et al., 7 Sep 2025).

The paper does not provide a detailed harmonic decomposition, but it reports that field distributions along the axis and near the bore were shown both numerically and experimentally. CST simulations indicate that the steel helices reshape the field so that near-axis behavior closely follows the ideal helical undulator field. Although end effects are necessarily present in an eight-period device, the infinite-helix formula is reported to give a satisfactory estimate even for a small number of periods down to $6$7. Measured and simulated field traces agree well both for external measurements and for near-axis scans in the single-helix and NdFeB-plus-steel test configurations (Magory et al., 7 Sep 2025).

A recurrent misunderstanding is that the hybrid device is merely a mechanically more complicated version of the two-helix NdFeB design. The reported comparison does not support that interpretation. The hybrid architecture changes both the achievable on-axis field and the external-field topology: it raises the field from above $6$8 T to about $6$9 T and simultaneously suppresses the outside field to near zero (Magory et al., 7 Sep 2025).

5. FEL and XFEL significance

The principal application context is compact FEL and XFEL operation, especially where beam energy is limited and interaction strength must be maximized with a very short-period undulator. The standard undulator parameter is written as

$50$0

with $50$1 taken as the rms magnetic field. For the planar case with $50$2, the rms field is $50$3; for the helical case $50$4. The paper further uses

$50$5

and

$50$6

Within this framework, the helical advantage appears directly through the larger helical undulator parameter and Pierce parameter at the same period and comparable field (Magory et al., 7 Sep 2025).

Using beam parameters derived from the ultra-compact XFEL concept of Rosenzweig et al., the reference hard UC-XFEL beam is taken to have electron energy $50$7 GeV, energy spread $50$8, microbunch charge $50$9 pC, rms bunch length $1$0 nm, peak current $1$1 kA, peak microbunch power $1$2 TW, and mean spot size $1$3 in the units given in the source table. Because the experimentally demonstrated field is $1$4 T at $1$5 mm, the comparison is made between modified planar and hybrid-helical configurations both at $1$6 mm period and $1$7 T peak field. The resulting parameters are: planar, $1$8, $1$9, $R_2=10$ 0 Å; hybrid helical, $R_2=10$ 1, $R_2=10$ 2, $R_2=10$ 3 Å (Magory et al., 7 Sep 2025).

In Genesis steady-state SASE simulations with the same strong-field FODO focusing system for both cases, the radiation powers reach $R_2=10$ 4 GW for the planar microundulator and $R_2=10$ 5 GW for the hybrid helical microundulator. The corresponding simulated wavelengths are $R_2=10$ 6 Å and $R_2=10$ 7 Å, and the reported radiation efficiencies are about $R_2=10$ 8 for the planar case and $R_2=10$ 9 for the helical case. If the energy spread is increased from $R_{2s}=4$ 0 to $R_{2s}=4$ 1, the outputs remain $R_{2s}=4$ 2 GW and $R_{2s}=4$ 3 for the planar case and $R_{2s}=4$ 4 GW and $R_{2s}=4$ 5 for the helical case. This is the basis for the reported ultra-compact SASE XFEL example in which the hybrid helical microundulator provides about $R_{2s}=4$ 6 GW at a wavelength of about $R_{2s}=4$ 7 Å (Magory et al., 7 Sep 2025).

A related but conceptually different helical-afterburner strategy was analyzed for LCLS, where a planar SASE undulator creates the microbunched beam and a short downstream $R_{2s}=4$ 8 m APPLE II helical radiator converts that preserved microbunching into few-GW coherent radiation at $R_{2s}=4$ 9 nm. In that beamline study, circular polarization above $1$00 is obtained by spatial filtering with Be slits placed after the APPLE II module (Geloni et al., 2011). This demonstrates that the helical advantage in FEL systems can arise either from a short helical after-radiator fed by preserved bunching or from a high-field helical microundulator used directly as the main short-period radiator; the two approaches address different implementation regimes.

The hybrid helical microundulator emerged from a staged development. The 2025 NdFeB prototype study experimentally validated the monolithic helical-undulator concept in a $1$01 mm-period, $1$02 mm-aperture two-helix device and explicitly sketched a four-helix Halbach-type helical micro-undulator together with a hybrid variant in which two radially magnetized helices are replaced by non-premagnetized steel or permendur-vanadium helices. That earlier paper stated that Halbach-type helical micro-undulators with periods of $1$03–$1$04 mm of four helices can provide a field of $1$05 T and $1$06–0.6 at the axis, but it did not build the hybrid version (Balal et al., 1 Aug 2025). The later prototype work advanced this concept to an experimentally demonstrated hybrid device with $1$07 mm period, $1$08 mm bore, and about $1$09 T on axis (Magory et al., 7 Sep 2025).

A broader hybrid lineage also includes the helical undulator based on partial redistribution of a uniform solenoidal field by a ferromagnetic helix. In that configuration, a solenoid supplies the main axial field and a ferromagnetic helical insertion partially redistributes the flux into a transverse helical undulator field. The reported analytical on-axis amplitude is

$1$10

and the experiment gave approximately $1$11 T at $1$12 T for a $1$13 cm-period steel helix (Balal et al., 2018). This is not a permanent-magnet microundulator, but it is directly relevant as a hybrid magnetic concept in which field production is shared between an external magnetic source and a shaped ferromagnetic helix.

The present prototype also makes its limitations explicit. The $1$14 mm aperture is both an advantage and a challenge: it supports strong field at short period but makes beam transport and field metrology difficult. The paper notes that obtaining $1$15 T at $1$16 mm period at room temperature would require an even smaller gap, of order $1$17 mm, which is impractical in the current approach. Fabrication of brittle NdFeB helices requires WEDM and careful handling during post-machining magnetization and assembly. Measurement uncertainty is dominated by sensor positioning in the tiny bore. The simple two-helix design has large stray field; the hybrid design remedies this at the cost of a somewhat more complex assembly. The paper does not discuss demagnetization in detail, but the use of axial premagnetization and steel flux redirection clearly avoids the harder problem of uniformly radially magnetized helices (Magory et al., 7 Sep 2025).

A plausible implication is that future work will focus less on proving the existence of the hybrid field topology and more on practical accelerator integration: beam transport through a $1$18 mm bore, phase-error control in longer devices, and extension of the demonstrated room-temperature architecture to shorter periods without collapsing the usable aperture. The reported results already establish the hybrid helical microundulator as a practical short-period architecture built from only four helices machined from solid stock, with a demonstrated combination of high on-axis field, near-zero outside field, and direct relevance to ultra-compact short-wavelength FELs (Magory et al., 7 Sep 2025).