Answers to Reviewers

Thank you very much for taking a lot of time and effort to comment on our paper. The comments help us to increase the quality of our work.

RC1

A detailed response to the many comments are found in the attached file.

Specific Comments

1. The motivation for the work should be strengthened by justifying the required accuracy of 0.2 nT within the context of the JUICE science mission. The motivation for this experiment appears to be a combination of instrument verification and determination of the ideal operating parameters and necessary post-processing. This motivation is discussed briefly in Section 4, but the manuscript would be improved by clearly stating this motivation and using it to justify the test configuration (Section 2).
   
   Reply: Currently, the J-MAG team is working on the instrument paper which will cover not only MAGSCA but also both fluxgate magnetometers. This paper will list all the relevant details concerning the JUICE missions for a broader scientific community and will explain how the requirements are defined. Our submitted manuscript aims to show that the required accuracy is achieved by MAGSCA and how it was measured since, the measurements and their evaluation are not straight forward. Nevertheless, we have added several annotations to the new version of our manuscript to explain and justify the 0.2 nT requirement for MAGSCA. Please check the detailed response to the many comments of reviewer 1 in the attached file. We have clarified the motivation at the beginning of section 2 of the new manuscript.
2. Throughout the work, the treatment of precision and accuracy is not clear. In some places the precision is defined as the standard deviation over measurements made at different angular orientations (e.g. line 114). In other places the precision seems to be defined as repeatability at a given sensor angle (e.g. line 89). In general, the conditions under which the expected or observed accuracy and precision are reported should be clearly stated. What (and how many) samples are combined to yield standard deviations? Also, are you assuming that a given level of repeatability during ground testing should provide the same level of repeatability in the spacecraft environment?
   
   Reply: In the new version of the manuscript we have tried to clarify the definitions of the used accuracy and precision. The heading characteristic defines the accuracy of the scalar magnetometer. The heading characteristic is an absolute error of MAGSCA depending on the orientation of the magnetic field vector in relation to the sensor axis. We distinguish between the accuracy of a measurement performed at a constant sensor angle and at a constant magnetic field strength and the "angular averaged accuracy" which is the mean value of all measurements performed for a heading characteristic (measured at equidistant sensor angles and constant magnetic field strength). The standard deviation of all measurements for a heading characteristic we define as "angular averaged precision". The sampling rates are added to the new manuscript. We are pretty sure that if the operational parameters (as used for the presented ground verification: such as vapour temperature and laser bias current) are re-established, the performance of MAGSCA will be the same during the space mission.
3. Sensor noise and sample rate are parameters of great interest to most magnetic sensing missions, but these considerations are not discussed at all in this work. Comparisons between MAGSCA and previous work would be more useful with additional information on sample rate or spectral noise.
   
   Reply: Please check the detailed response to your comments in the attached file. We added the sampling rate and noise level. I want to emphasize that the instrument paper will cover this topic in greater detail since also the performance of both fluxgate magnetometers will be of great significance for the scientific community.
4. The observed performance in this experiment is demonstrated to be sufficient for the JUICE mission requirement, but without discussion of the source of this requirement the significance of this experiment to the broader JUICE mission and scientific community is not clear.
   
   Reply: Please see response to "specific comment 1" and the detailed response in the attached file.
   
   

RC2

1. The Heading characteristic seems to be an offset error – independent of ambient field magnitude. It is mentioned in chapter 1.1/1.2 as absolute error, which depends on laser bias current and rubidium vapour temperature. Please add here the independence on field strength.
   
   Reply: The manuscript shows that the independence from the magnetic field strength is achieved in the magnetic field strength range (300 to 1500 nT). The manuscript also discusses the highly linear relationship between the detection frequency and the magnetic field strength. However, for larger magnetic field strength (in Earth's magnetic field range (Pollinger et. al. 2020)) second order effects impact the heading characteristics (see response to comment 3 of RC2) where the offset error can change. Thus, it is - in general - not true that the offset error is independent of the ambient field magnitude.
2. In the error discussion two error quantities are introduced, angular averaged precision (standard deviation to nominal field value) and angular averaged accuracy (averaged displacement of measurement to nominal field). The second error quantity is probably introduced because the heading error leads generally to an underestimate of the field magnitude. Is there any physical reason, that the measured value is in average lower than the real field magnitude? If yes, please indicate.
   
   Reply: This offset is assumed to be a result of light shift effects. The light shifts are atomic level shifts caused by the interaction of the laser light with the atomic states. The mentioned direct laser current modulation creates a complex laser light spectrum for the excitation of the CPT resonances. The precise impact of each of these light fields (at different frequencies) on each atomic level (participating in the formation of the CPT resonances) cannot be modelled easily. Under certain conditions, light shifts are indistinguishable from Zeeman shifts (= atomic level shifts created by the ambient magnetic field). However, the measurement principle of MAGSCA is designed to minimise these light shifts. The residual light shifts appear as heading characteristics of the magnetometer. It is assumed that the imbalance of the individual components of the laser light spectrum together with their frequency detuning to their respective atomic transitions cause the offsets of the magnetic field strength measurement. The discussion of light shift effects is a very complex one, thus it was found to be not the scope of this work. A detailed discussion of the heading characteristics is found in (Amtmann 2022).
3. In chapter 2 the measurement setup in the COBS facilities is described. A coil system is used for compensating the Earth field and for setting artificial test fields. Since the homogeneity inside the test volume is limited, additional errors have to be taken into account (AEcoil and Pcoil). This could simply be avoided by investigating the heading error in the very homogeneous and known field in the observatory - without any coil system and similar to tests performed with proton magnetometers.  Please add a sentence why the coil system facility has been used.
   
   Reply: The Merritt coil system was used since it allows verifying MAGSCA at the magnetic field strengths of 300 to 1500 nT required for the Ganymede phase (compared to the Earth's magnetic field strength 48000 nT). For larger magnetic field strengths (> 10000 nT) the MAGSCA measurement principle requires an internal reference frequency correction (as it was used for (Pollinger et. al. 2020)) which is not implemented within MAGSCA. The higher magnetic field strength can have an impact on the heading characteristics and its offset (see response to comment 1).
   
   Additionally, the Merritt coil system allows (compared to the manual rotation of the sensor unit in the Earth's magnetic field) for much faster measurements, which increased the parameter space which can be sampled in a feasible time frame. We have added an annotation (line 167 to 168 of the new manuscript) to clarify that we need the Merritt coil system to apply magnetic fields in the required range for the JUICE mission.