Ignition and onitoring technique for plasa processing of ulticell superconducting radio frequency cavities Marc Doleans Oak Ridge ational Laboratory, Oak Ridge, Tennessee 3783, USA E ail: doleans@ornl.gov ABSTRACT An in situ plasa processing technique has been developed at the Spallation eutron Source (SS) to iprove the perforance of the superconducting radio frequency (SRF) cavities in operation. The technique uses a low density reactive neon oxygen plasa at roo teperature to iprove the surface work function, to help reove adsorbed gases on the RF surface and to reduce its secondary eission yield. SS SRF cavities have six accelerating cells and the plasa typically ignites in the cell where the electric field is the highest. This article details the technique to ignite and onitor the plasa in each cell of the SS cavities. Keywords: Plasa processes, Radiofrequency discharges, Superconductivity, Particle accelerators. ITRODUCTIO The SRF cavities at the SS are operated at 85 MHz in pulsed ode with 6 Hz repetition rate []. The cavities are packaged in cryoodules hosting 3 or 4 cavities cooled down to K during neutron production. The average accelerating gradient of the 8 cavities installed in the linear accelerator (linac) tunnel is.5 MV/. Theral instabilities at the extreities of the cavities induced priarily by field eitted electrons prevent fro operating cavities at higher accelerating gradients []. In situ plasa processing is being progressively applied to the SS SRF cavities at roo teperature during the scheduled aintenance periods of the accelerator to help iproving their accelerating gradients [3,4]. For the plasa generation in SS SRF cavities, neon gas is introduced in the cavity volue and an RF discharge is initiated by connecting the plasa processing RF station to the fundaental power coupler and exciting the TM fundaental passband odes of the cavity. The RF station uses a solid state aplifier and concoitant RF systes with enough bandwidth to excite any of the TM odes of the SS 6 cell cavities. In this article, a cavity odel to obtain the aplitude of the electric field in each cell of an SRF cavity with nearest neighbor coupling is first presented. The eigen analysis for ultiple cell cavities is reviewed and the odel is extended to include RF driving ters and off resonance excitation. The odel is applied to SS high beta cavities and off resonance excitation is shown to be effective to control the relative aplitudes of the cells of the cavities. To copleent off resonance excitation,
dual tone excitation where the signals fro two independent RF generators are cobined to drive a cavity is used and the schee to ignite the plasa in each of the cells of the SS cavities is detailed. Finally, to onitor the location of the plasa inside the cavity volue when direct optical observation is unavailable, like during in situ plasa processing of cryoodules in the linac tunnel, the effect of the plasa is included in the cavity odel. It is shown that the signal fro a field probe located at one extreity of each cavity can be used to infer the location of the plasa inside the cavity volue.. CAVITY MODEL The TM passband odes of an cell elliptical cavity can be odeled using a series of weakly coupled linear haronic oscillators. The frequency and relative aplitude of the accelerating field in the cells for the passband odes are the eigen solutions of a linear syste of undaped hoogeneous equations A () where = is the index for the odes, A is an x atrix containing the weak coupling factor k between adjacent cells and and are the eigen value and eigen vector for the th ode respectively. The atrix A is given by [5] 3k k A k k k k k k k k k 3k () The eleents of the x eigen vector are the relative aplitudes of the accelerating field in the cells for the th ode. The eigen values are related to the ratio of the ode frequencies f and the frequency f for a single cell with etallic boundary condition (3) with =f. The general solutions for the ode frequencies and noralized aplitudes of Equation () are [5] k cos V j sin j / (4)
Where the eleents V j are eleents of a x unitary atrix with and j indexes referring to the th ode and j th cell respectively, and where is the Kronecker delta. The rows of the V atrix are the transposed of the eigen vectors. V T T T V V (5) The eigen vectors for an orthogonal set, i.e. T n n (6) The eigen solutions of Equation () give the frequencies and relative aplitudes of excitation for the cells for the fundaental odes. A ore coplete odel is necessary to get the cell aplitudes over the full frequency spectru and with the cavity RF wall dissipation and RF driving ters included. Introducing a x driving vector D with each eleent representing a possible RF drive for each of the cells and assuing that the quality factor Q is the sae for all the cells one gets for odel equation A j Q I Y D (7) Where A is the atrix described above, I is the x identity atrix, D is the RF driving vector, and where Y is the new vector solution at the driving frequency. In the previous equation it was assued that the RF wall dissipation doinates the tie constant of the cavity which is a good approxiation for SRF cavities at roo teperature where the plasa processing is perfored. It should be pointed out that D plays the role of a driving current and is thus proportional to the square root of the RF driving power. Perturbation theory can be applied to find an analytical expression for the solution vector Y as a linear coposition of the eigen vectors of the hoogeneous equation, i.e. Y c (8) The coefficients c can be deterined analytically by inserting Equation (8) into Equation (7). One gets c j D Q (9) Multiplying each side by T and using the orthogonality relation fro Equation (6) leads to 3
4 D Q j c T () The result of Equation () can be inserted into Equation (8) to obtain an analytical solution for the driven aplitude in the cells at any frequency. T D Q j Y () An SRF cavity is typically driven by a power coupler at one end of the structure. Assuing the power coupler drives the first cell of the structure, one can define T D () and finds that the aplitude of excitation for the th ode (i.e. pi ode) fro Equation () is in good approxiation equal to Q /. The result of Equation () can be noralized so that the aplitude for the th ode is equal to unity. After inserting Equation () in Equation () and noralizing one gets Q j Q Y sin ~ (3) The usual cavity paraeters can be used to get the vector solution for the aplitude of the accelerating field in the cells ) ( ~ 4 Y P Q Q r L E g acc (4) where L is the noralization length for the accelerating field, where r/q is the shunt ipedance of the cavity, where =Q /Q ex is the coupling ratio between the quality factor of the cavity and the external quality factor of the power coupler and where P g is the power of the RF generator driving the ulticell cavity. 3. APPLICATIO OF THE MODEL TO THE TO SS HIGH BETA CAVITIES Equations (3) and (4) can be used to calculate the paraeters f and k using the resonant frequency of the first ode f and the resonant frequency of the th ode f (pi ode) of a cavity
f f f f k cos / 3 cos / f f 4k (5) Table suarizes the paraeters for an offline SS high beta cavity at roo teperature. As shown in Table, the frequency of the pi ode is lower at roo teperature than at K where the cavity is operated at 85 MHz. The values in Table can be used into Equation (4) to find the eigen solutions and for the cavity. The results are illustrated in Figures and. Table : Paraeters for an SS six cell high beta cavities at roo teperature 6 cells f 84.73 MHz f 79.648 MHz k.587% f 79.87 MHz L.96 Q 9.5 3 at 93 K Q ex 7.3 5 r/q 47 Oh Figure : Eigen values for the six fundaental odes of an SS high beta cavity. A cosine curve is also plotted to guide the eye. 5
Figure : Eigen vector for the six fundaental odes of an SS high beta cavity. The 6 th ode, socalled pi ode, is the ode used for bea acceleration. Paraeters fro Table can be inserted into Equation (3) to get the spectru of excitation for each cell of the SS high beta cavity. The result is illustrated in Figure 3(a). In this figure, the six fundaental odes of the structure can be observed with the pi ode being the ode with the highest frequency at 84.73 MHz. 6
As entioned in Section, the RF power coupler is driving cell. A field probe near cell 6 is used to onitor the aplitude of the accelerating field in the SS cavities. The spectru of excitation of cell 6 obtained fro the odel and fro a direct S easureent in an offline SS high beta cavity using a spectru analyzer with port connected the power coupler and port connected to the field probe are shown in Figure 3(b). Since the S easureent is a ratio between powers transitted through port and forwarded fro port, the square root of the S signal was taken to obtain a signal proportional to the field aplitude. To copare the spectra fro the experient and fro the odel, the signal fro the experient was also scaled such that it is equal to unity at the pi ode resonant frequency. As seen fro Figure 3(b) the spectru of excitation for cell 6 obtained fro the odel is in reasonable agreeent with the experiental spectru indicating that the odel can be used to quantify the field aplitude for each cell of the SS cavities over the full frequency spectru. Figure 3: (a) Spectra of the cell aplitudes obtained fro the cavity odel for each cell of an SS highbeta cavity at roo teperature. (b) Spectra of excitation for cell 6 fro the experient and fro the cavity odel. Figure 4 shows the cell aplitudes obtained fro the odel near each resonant ode in ore details. Assuing the surface condition is hoogeneous in a cavity, the plasa ignites in the cell with the highest electric field. Because of the syetry of the structure, there are always two cells or ore with equal aplitudes when the cavity is driven at the resonant frequency of any fundaental ode. 7
Figure 4: cell aplitudes near each resonant ode of an SS high beta cavity For exaple, all six cells have the sae aplitude when the cavity is driven at the pi ode resonance as illustrated in Figures and 4. This degeneracy prevents fro deterinistically igniting a plasa in each cell of a cavity when using on resonance excitation only. Off resonance excitation provides a eans to introduce an asyetry in the cell aplitudes. For exaple, the last plot of Figure 4 indicates that while 8
the cell aplitudes are identical at the pi ode resonance, the degeneracy is resolved once the cavity is driven below or above the pi ode frequency. Below the pi ode frequency, cell 6 has the highest field and cell has the lowest field. The opposite is true when the cavity is excited at a frequency above the pi ode. Figure 5: Asyetry between pair of cells near each resonant ode of an SS high beta cavity 9
For a cavity with an even nuber of cells like the SS SRF cavities, the degeneracy of cell aplitudes occurs at all resonant frequencies for the pair of cells and 6, and 5, and 3 and 4.Thus, it is iportant to quantify how uch field asyetry can be generated for those pairs of cells by using off resonance excitation as illustrated in Figure 5. The half bandwidth in SS cavities at roo teperature is in the order of 4 khz with the half bandwidth (hbw) defined with respect to the frequency f and to the quality factor Q as hbw = f /Q. Fro Figure 5 one can see that exciting a ode off resonance by one to several half bandwidths can generate a significant aount of asyetry between cell aplitudes. For exaple, exciting the first ode 4 khz below its resonance frequency generates approxiately 3% of asyetry between the aplitudes of cell and cell 6. But, exciting a ode off resonance is inefficient and additional RF power is required to reach the sae field aplitude than on resonance. In addition, a ode that generates a lot of asyetry for a given pair of cells is not always efficient to generate a large aount of field in those cells. In the previous exaple, ode can generate a large aount of asyetry between cells and 6 but is intrinsically a poor choice to efficiently generate field in those cells. Instead of relying on a single ode to generate a large aount of field as well as generating asyetry between cell aplitudes, a schee with dualtone excitation is used at the SS to achieve plasa ignition in each cell of a cavity. 4. DUAL TOE ECITATIO In the dual tone excitation technique, the signals fro two RF generators are cobined, aplified by a broadband solid state aplifier and forwarded to a cavity through the fundaental power coupler. As described in Section 3, having two independent driving frequencies yields a frequency of excitation to efficiently generate an electric field in the cells and a second frequency to generate asyetry between a desired cell and its irror iage (i.e. cell and 6, cell and 5, cell 3 and 4 for SS cavities). Because the frequencies fro the two RF generators are different, envelope beating occurs. Assuing a field is excited in the cavity at two different frequencies and and with respective aplitudes a and a, the total electric field is the su j t jt E a e ae (6) Because the difference between the two frequencies that are used in the dual tone excitation technique is uch saller than the average frequency it is convenient to decopose the electric field in a fast oscillating coponent at the average frequency and a slower envelope coponent ~ oscillating at the frequency =( )/ E jt jt jt jt a a e ~ e After introducing the angles (7)
( t) t a tan a (8) the nor of the envelope is given by a a (9) where the tie dependent coefficient is defined as sin cos () The iniu and axiu values for the envelope are a a sin () ax in The tie averaged value for is given by sin cos d () Equation () can be expressed analytically in ters of elliptical integrals or approxiated by a sipler analytical function as 3 sin a a (3) The stored electrical energy in a cell is proportional to the square of the electrical field aplitude and its average over tie is proportional to a a (4) Experients at SS indicate that the plasa ignition scales according to Equation (4) for dual tone excitation. 5. PLASMA IGITIO I EACH CELL OF SS HIGH BETA CAVITIES The absolute ignition level depends on paraeters such as gas coposition and gas pressure as shown in Figure 6. During the fabrication process of the SS high beta cavities, only the pi ode was precisely tuned and the field flatness for the pi ode is 8% or better [6], with the field flatness defined as the difference in aplitude between the cells with the highest and lowest fields, divided by the averaged aplitude over all the cells.
Figure 6: Ignition curve for neon gas in an SS six cell high beta cavity. The cavity is driven at the piode resonance. Because the pi ode was precisely tuned for all SS cavities the driving power of an RF generator to ignite a plasa at the pi ode resonant frequency is used as a reference. If one expresses the driving powers p RF and p RF for two RF generators with respect to that reference one can write a relevant paraeter for plasa ignition as ~ ~ p Y (5) j RF j p Y RF j j in Equation (5) is the equivalent of the paraeter fro Equation (4) for the j th cell when a cavity is driven using dual tone excitation. Reaching an aplitude of one for j corresponds to plasa ignition in the j th cell. Table : Paraeters for the ignition in each cell of an SS high beta cavity using the cavity odel. The grayed value in each row denotes ignition level for a cell. cell RF gen. f p RF RF gen. f 3 4 5 6 ignition (hbw) (db) (hbw) (db) ode 5. 4.57 ode 6 +.5 3.46..7.4.37.6.9 ode.. ode 5.5.87.74..4.8.88.69 3 ode..8 ode 3.5 4.5.88.8..9.89.78 4 ode..63 ode 4.5.79.77.6.9..6.69 5 ode..3 ode 6.5.99.7.88.36.4..44 6 ode 5. 8.6 ode 6.5.3.8.6.44.49.75. p RF Equation (5) was used to find paraeters (frequency and driving power) for two RF generators such that ignition can be achieved in each cell of the SS high beta cavities. Table suarizes the
corresponding settings, drive frequency f and drive power p RF for both RF generators. The frequencies f are detuning with respect to the specified resonant odes and are expressed in unit of halfbandwidths. The drive powers p RF are given in db. Each row in Table corresponds to a possible ignition condition for a specific cell. As shown in Figure 3, the odeled excitation spectru for a cavity is reasonably close to the spectru easured experientally. But, correction factors can be introduced for increased accuracy. The correction factors for the odel can be defined by coparing the driving power required to ignite a plasa at each resonant frequency experientally to the one fro the odel. However, as the cavity is excited by a single RF generator at each ode resonant frequency, degeneracy of the cells aplitudes prevents fro controlling where the plasa ignites. Table 3 shows correction factors P for each ode of the high beta cavity introduced in Section 3. As explained above, ignition at the pi ode resonant frequency is used as the reference and thus the correction factor for the sixth ode is null. The experiental values in Table 3 were easured for torr of neon pressure in the cavity. In this condition, the absolute driving power for the RF generator to ignite the plasa at the pi ode resonant frequency, P ode, was 4.4 db as shown in Figure 6. Table 3: Driving power for an RF generator to ignite a neon plasa in an offline SS high beta cavity at the resonant frequency of each passband ode. The pi ode is used as reference. The last two coluns show the correction factors to be used in the cavity odel for increased accuracy. Mode ignition p RF odel (db) p RF experient (db) P (db) P 6. 4.4.6 3%... % 3.3.4.43 9% 4 3.45 4..55 % 5 5.33 4.9.43 % 6 reference reference. % The values for the driving powers fro Table and the correction factors fro Table3 can be used to refine the estiates in the odel for igniting a plasa in each cell of the considered SS high beta cavity using dual tone excitation. For each cell ignition, the absolute driving power for an RF generator, P RF, is obtained by suing the reference power P ode for igniting a plasa at the pi ode resonant frequency, the value p RF fro Table and the appropriate correction factor P fro Table 3. P RF P od e p RF P (6) 3
The values of the driving power for both RF generators, P RF and P RF, obtained fro the odel after applying Equation (6) are suarized in Table 4. The absolute frequency of excitation for both generators using the ode frequencies and the detuning fro Table are also listed. The plasa ignition levels were found experientally by starting both RF generators 3 db below their estiated values fro the odel and slowly increasing their drive power until ignition of a plasa was reached. Once the plasa was ignited, the experiental values of the RF generator driving powers were recorded and the cell where the plasa had ignited was copared to the predicted location fro the odel. The error between the driving power of the RF generators found experientally and estiated using the cavity odel is shown in the last two coluns of Table 4. As shown in this Table, the plasa has ignited in the cells predicted by the odel and the drive paraeters estiated in the odel are reasonably close to the ones found experientally. Table 4: Settings for the RF generators to ignite a neon plasa at Torr pressure using dual tone excitation. The error between the drive power of the RF generators found experientally and estiated using the cavity odel is shown in the last two coluns in db and in %. f RF P RF odel f RF P RF odel cell ignited in error error (MHz) (db) (MHz) (db) experient (db) 83.4.7 84.93.94.57 % 794.965.38 83.36 5.7.8 % 79.648. 798. 8. 3.5 % 79.648 3.43 8.88 6.65 4.3 % 794.965 3.6 84.73 5.39 5.6 % 83.46 3.43 84.3 4.7 6.37 8% 6. MOITORIG OF THE PLASMA AFTER IGITIO The previous sections presented a odel for the SS high beta cavities and its use to control the ignition of a plasa in each cell of the SS high beta cavities. This technique has been applied successfully to offline cavities and to online cavities in cryoodules in the linac tunnel. For offline cavities, direct onitoring of the plasa in a cavity was done using caeras ounted on the bea axis as explained in [3]. Figure 7 shows pictures of a plasa in each cell of a high beta SS cavity using the off resonance and dual tone excitation technique presented in Section 5. For online cavities, the plasa inside the cavity volue can t be onitored optically. onetheless the signal fro the field probe can be used to gain inforation about the location of the plasa. 4
Figure 7: eon plasa iaged in each cell of a six cell SS high beta cavity as iaged by a caera ounted on the bea axis and at the left side of the cavity. Once a plasa is ignited inside the cavity volue, it acts as a dielectric and changes the resonant frequency of the structure [7]. The odel presented in Section can be extended to include the case where a plasa shifts the resonant frequencies of the cells. To this effect a new ter is added to Equation (7) A j Q I Z D (7) In Equation (7), the vector solution was changed fro Y to Z to distinguish it fro the case without plasa ignited inside the cavity volue. The new atrix is a diagonal atrix defined as (8) where the diagonal eleents j are related to the dielectric constant j in the j th cell by j j (9) Equation (7) can be solved using the sae perturbation technique than the one used in Section, i.e. looking for solutions as 5
6 Z c (3) The coefficients c can be conveniently written in a vector for T c c C (3) And the solution to this vector is given by SM C (3) where the vector S is D D S T T T (33) And where M is a x atrix defined as M M M (34) with Q j Q j M (35) and T T T T M (36) Close attention should be given to the inversion for the M atrix in Equation (3) as the sall ters can generate nuerical noise. As done in Section, the vector solution can be noralized so that the aplitude at the pi ode in absence of any plasa is equal to unity Z Q Z ~ (37) A siple shift can then be used so that the results fro the odel can be copared to experiental results. For exaple, in absence of any plasa, the power easured experientally through the field probe located at cell 6 in the cavity fro Section 3 is 4.8 db for 3 W of forwarded power at the pi
ode resonant frequency. The power P j for the j th cell in the odel can be atched to the experient by using the result of Equation (37) with a corresponding shift ~ P ( db) log Z 4.8 (38) j j The cell powers P j can be interpreted as signals fro virtual field probes in each cell of a cavity. Experientally, only cell 6 is being onitored using a field probe. The cell powers obtained fro the odel near the pi ode frequency in absence of any plasa are shown in Figure 8. Figure 8: Results fro the cavity odel showing the cell powers in each cell of an SS high beta cavity near the pi ode in absence of any plasa. To verify the accuracy of the odel when a plasa is ignited, one considers the case of the SS highbeta cavity introduced in Section 3 with each cell ignited sequentially using the dual tone excitation technique described in Section 5. After ignition of the plasa in each cell using dual tone excitation, one RF generator is turned off and the other is changed to a frequency of 84.573 MHz, 3 khz above the pi ode resonance, and with a driving power corresponding to 3 W of forwarded RF power. After the plasa is ignited, the frequency of the cell where the discharge occurs shifts upward [7] and, if the drive frequency is kept constant, the aplitude of the field in the cavity decreases until stabilization of the plasa density is reached. The stabilization occurs when the net change of electron density in the plasa is null, i.e. when the aount of new electrons generated is equal to the aount of electrons lost per unit tie. One can find the stabilization condition experientally when discharging in cell 6 of the cavity which has a field probe onitoring the field aplitude. One finds that the field probe indicates. db after the plasa has ignited and stabilized in cell 6. This reference value can be used in the odel to find the value of the paraeter in Equation (7) such that the cell power where the discharge occurs is equal to. db at the driving frequency of 84.573 MHz. The cell powers fro the virtual field probes fro the odel are illustrated in Figure 9. 7
Coparing the results fro Figures 8 and 9 one can see that the plasa significantly affects the excitation spectru of a cavity. In particular, one can see that for the pi ode, the field in the cell where the discharge occurs tends to increase relative to the field in the other cells. Figure shows the field probe power fro the experient and fro the odel for a drive frequency equal to 84.573 MHz and for 3 W of forward power. Figure 9: Modeled cell powers in each cell of an SS high beta cavity near the pi ode for a given value of in each cell. The values for were deterined such that the power in the corresponding cell is 8
equal to. db at the drive frequency of 84.573 MHz (arked with a star). Modeled field probe powers at that frequency are arked with a triangle and those values are suarized in Figure. The result fro the odel is in good agreeent with the result fro the experient and shows that the field probe signal can be used to verify the location of the plasa in the cavity when direct optical onitoring isn t available. This localization ethod is successfully used at the SS when plasa processing is perfored in situ in the linac tunnel. Figure : Field probe power for an SS high beta cavity when a plasa is ignited in each cell. The RF generator is set at a frequency of 84.573 MHz with 3 W of forward power. 7. COCLUSIO In situ plasa processing is a new cleaning technique developed and used at the SS to iprove the perforance of superconducting RF cavities. This article presented a technique to generate and onitor a plasa in the SS six cell elliptical cavities. Experiental results showed that this technique is successful to control and onitor the location of the plasa ignition inside the cavity volue. Siilar ignition and onitoring technique could be envisaged for the plasa processing of other ulticell superconducting RF cavities. Basic paraeters such as frequency, nuber of cells and coupling paraeter need to be adjusted in Section 3 to generate suitable cavity odels. Paraeters in Section 5 for dual tone excitation could then be investigated to estiate how uch asyetry between cells can be achieved for other cavity geoetries. The technique described in this article is being applied for in situ plasa processing of the SS cryoodules during aintenance periods of the accelerator to increase the output bea energy. The 9
results pertaining to the plasa processing of cryoodules and iproveent of their perforance will be published separately. 8. AKOWLEDGMET Many thanks to y colleagues fro the superconducting linac systes and accelerator physics groups at the SS for useful discussions and suggestions during the redaction of this anuscript. This anuscript has been authored by UT Battelle, LLC under Contract o. DE AC5 OR75 with the U.S. Departent of Energy. 9. REFERECES [] S. Henderson et al., The Spallation eutron Source accelerator syste design, uclear Instruents and Methods in Physics Research, Section A: Accelerators, Spectroeters, Detectors and Associated Equipent, vol. 763 (4). [] S. Ki, Status of the SS Superconducting Linac and Future Plan, J. Korean Phys. Soc. 5 (8) 74. doi:.3938/jkps.5.74. [3] M. Doleans, P.V. Tyagi, R. Afanador, C.J. McMahan et al., "In situ plasa processing to increase the accelerating gradients of superconducting radio frequency cavities", uclear Instruents and Methods in Physics Research A, 8 (6) 5 59. doi:.6/j.nia.5..43. [4] P.V. Tyagi, M. Doleans, B. Hannah, R. Afanador, C.J. McMahan et al., " Iproving the work function of the niobiu surface of SRF cavities by plasa processing", Applied Surface Science 369 (6) 9 35. [5] H. Padasee, J. Knobloch, T. Hays, RF superconductivity for accelerators, John Wiley & Sons, Inc., 8. [6] SS Paraeters List, SS PL R3 (5). [7] M. Doleans et al., Plasa processing R&D for the SS superconducting linac RF cavities, in Proceedings of SRF Conference, 3.