Scientific usage of the Pencil Code

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August 23, 2025

Figure 1: Number of papers since 2003 that make use of the Pen- cil Code. In red is shown the number of papers that reference it for code comparison or other purposes and in blue the papers that are not co-authored by Brandenburg. The enhanced number of pa- pers during 2011–2013 results from publications related to his ERC Advanced Grant. A search using ADS https:

//ui.adsabs.harvard.edu/ lists

the papers in which the Pencil Code is being quoted. In the following we present the papers that are making use of the code either for their own scientific work of those authors, or for code comparison purposes. We include conference proceedings, which make up 15–20% of all papers. We classify the references by year and by topic, although the topics are often overlapping. The primary application of the Pencil Code lies in astrophysics, in which case we classify the papers mostly by the field of research. Additional applications can also be found in meteorology and combustion.

1 Papers by year

As of September 2024, the Pencil Code has been used for a total of 736 research papers; see Figure 1; 379 of those are papers (51%) are not co-authored by Brandenburg. In addition, 138 papers reference it for code comparison or other purposes (see the red line).

33 times in 2025 (Koshikumo et al., 2025; Vachaspati and Brandenburg, 2025; Godines et al., 2025; Iarygina et al., 2025; Srivastava et al., 2025; Hidalgo et al., 2025; Shchutskyi et al., 2025; Sabelnikov et al., 2025; Tschernitz and Bourdin, 2025; Hosking et al., 2025; Yuvraj et al., 2025; Kishore and Singh, 2025b; Warnecke et al., 2025; Brandenburg and Scannapieco, 2025; Käpylä, 2025; Brandenburg et al., 2025b; Brandenburg and Vishniac, 2025; Singh et al., 2025; Rogachevskii et al., 2025; Brandenburg et al., 2025a; Sharma et al., 2025b; Brandenburg and Ntormousi, 2025; Mondal et al., 2025; Rice et al., 2025; Qazi et al., 2025; Pandey and Bourdin, 2025; Meftah, 2025; Park, 2025; Roper Pol and Salvino Midiri, 2025; Brandenburg et al., 2025c; Eriksson et al., 2025; Dehman and Brandenburg, 2025; Shi et al., 2025),

40 times in 2024 (Candelaresi and Del Sordo, 2024; Brandenburg and Banerjee, 2025; Maity et al., 2024a; Zhou and Lai, 2024; Lipatnikov, 2024a; Vemareddy, 2024; Hidalgo et al., 2024; Schäfer et al., 2024; Elias-López et al., 2024; Dwivedi et al., 2024; Kesri et al., 2024; Kishore et al., 2024; Dey et al., 2024; Lipatnikov, 2024b; Vashishth, 2024; Maity et al., 2024b; Korpi-Lagg et al., 2024; Lyra et al., 2024; Mtchedlidze et al., 2024; Brandenburg and Banerjee, 2024; Sengupta et al., 2024; Saieed and Hickey, 2024; Wang et al., 2024; Iarygina et al., 2024; Schober et al., 2024a,b; Gent et al., 2024; Zhou, 2024; Zhou and Blackman, 2024; Qazi et al., 2024; Zhou and Jingade, 2024; Hackman et al., 2024; Kirchschlager et al., 2024; Cañas et al., 2024; Brandenburg et al., 2024a,b,c; Vemareddy et al., 2024; Käpylä, 2024; Zhou, 2024),

39 times in 2023 (Carenza et al., 2023; Väisälä et al., 2023; Sharma et al., 2023; Candelaresi and Beck, 2023; Zhu and Shi, 2023; Ganti et al., 2023; Mondal and Bhat, 2023; Brandenburg and Protiti, 2023; Pavaskar et al., 2023; Karak, 2023; Käpylä et al., 2023; Ortiz-Rodríguez et al., 2023; Tharakkal et al., 2023a,b; Navarrete et al., 2023; Lipatnikov and Sabelnikov, 2023; Warnecke et al., 2023; Brandenburg and Larsson, 2023; Elias-López et al., 2023; Lyra, 2023; Hidalgo et al., 2023; Mizerski et al., 2023; Yuvraj et al., 2023; He et al., 2023; Brandenburg et al., 2023a,b,c,e,d; Brandenburg, 2023a,b; Mtchedlidze et al., 2023; Park et al., 2023; Zhang et al., 2023; Sengupta and Umurhan, 2023; Gent et al., 2023; Meftah, 2023; Käpylä, 2023a,b),

38 times in 2022 (Maity et al., 2024a; Dey et al., 2022; Chatterjee and Dey, 2022; Becerra et al., 2022a; Tschernitz and Bourdin, 2022; Li et al., 2022; Käpylä and Singh, 2022; Ortiz-Rodríguez et al., 2022; Hyder et al., 2022; Zhou et al., 2022; Masada and Sano, 2022; Lipatnikov and Sabelnikov, 2022; Käpylä et al., 2022; Yang and Zhu, 2022; Roper Pol, 2022; Sharma and Brandenburg, 2022; Brandenburg and Ntormousi, 2022; Navarrete et al., 2022; AlbertoRoper, 2022; Baehr et al., 2022; Stejko et al., 2022a,b; Currie et al., 2022a; Roper Pol et al., 2022b; Mtchedlidze et al., 2022; Currie et al., 2022b; Bhatnagar et al., 2022; Haugen et al., 2022; Becerra et al., 2022b; Maiti et al., 2022; Schober et al., 2022a,b; Käpylä, 2022; Kirchschlager et al., 2022; Bhat, 2022; Roper Pol et al., 2022a; Mattsson and Hedvall, 2022; Pekkilä et al., 2022; Karchniwy et al., 2022), 47 times in 2021 (Barekat et al., 2021; Yang and Zhu, 2021; Käpylä, 2021a; Kahniashvili et al.,

2022; Bhat, 2021; Mattsson and Hedvall, 2021; Zhou and Blackman, 2021; He et al., 2021b; Bhatnagar et al., 2021; Kirchschlager et al., 2021; Hyder et al., 2021; Brandenburg and Sharma, 2021; Warnecke et al., 2021; Prabhu et al., 2021; Brandenburg and Das, 2021; Schaffer et al., 2021; Maiti et al., 2021; Roper Pol et al., 2022b; Brandenburg et al., 2021a,d,b; Käpylä, 2021b; Becerra et al., 2021; Oliveira et al., 2021; Raettig et al., 2021; Roper Pol, 2021; Haugen et al., 2021a,b; He et al., 2021a; Gent et al., 2021; Klahr and Schreiber, 2021; Li and Mattsson, 2021; Kahniashvili et al., 2021; Pencil Code Collaboration et al., 2021; Santos-Lima et al., 2021; Navarrete et al., 2021; Jakab and Brandenburg, 2021; Baehr and Zhu, 2021a,b; Brandenburg et al., 2021c; Zhu and Yang, 2021; Bhat et al., 2021; Zhuleku et al., 2021; Viviani et al., 2021; Park and Cheoun, 2021; Viviani and Käpylä, 2021; Väisälä et al., 2021),

41 times in 2020 (Barekat et al., 2020; Hyder et al., 2020; Brandenburg et al., 2020b; Park, 2020; Klahr and Schreiber, 2020; Brandenburg and Furuya, 2020; Rüdiger et al., 2020; Willamo et al., 2020; Candelaresi and Del Sordo, 2020; Zhang et al., 2020; Navarrete et al., 2020; Pusztai et al., 2020; Brandenburg, 2020a,b; Li and Mattsson, 2020; Adrover-González and Terradas, 2020; Brandenburg and Brüggen, 2020; Gerbig et al., 2020; Seta et al., 2020; Brandenburg and Boldyrev, 2020; Bhatnagar, 2020; Eriksson et al., 2020; Käpylä et al., 2020a,b; Aarnes et al., 2020; Qian et al., 2020; Gent et al., 2020; Schober et al., 2020a,b; Roper Pol et al., 2020a,b; Brandenburg and Das, 2020; Singh et al., 2020; Chatterjee, 2020; Bourdin, 2020; Warnecke and Bingert, 2020; Brandenburg and Chen, 2020; Navarrete et al., 2020; Li et al., 2020; Brandenburg and Scannapieco, 2020; Kahniashvili et al., 2020),

39 times in 2019 (Peng et al., 2019; Evirgen and Gent, 2019; Park, 2019a,b; Rüdiger et al., 2019; Gerbig et al., 2019; Warnecke and Peter, 2019b,a; Käpylä, 2019; Evirgen et al., 2019; Peng et al., 2019; Viviani et al., 2019; Bhat et al., 2019; Nauman and Nättilä, 2019; Castrejon et al., 2019; Candelaresi et al., 2019; Baehr and Klahr, 2019; Rodrigues et al., 2019; Hernandez et al., 2019; Li et al., 2019; Aarnes et al., 2019b; Smiet et al., 2019; Brandenburg et al., 2019a,b; Brandenburg and Rempel, 2019; Käpylä et al., 2019; Mattsson et al., 2019b,a; Losada et al., 2019; Seta and Beck, 2019; Rempel et al., 2019; Manser et al., 2019; Yang and Zhu, 2020; Mao et al., 2019; Hedvall and Mattsson, 2019; Schober et al., 2019; Brandenburg, 2019a,b; Aarnes et al., 2019a; Karchniwy et al., 2019),

32 times in 2018 (Käpylä et al., 2018; Väisälä et al., 2018; Warnecke, 2018; Warnecke et al., 2018; Li et al., 2018b; Schober et al., 2018; Käpylä, 2018; McNally et al., 2018; Zhang et al., 2018b; Schaffer et al., 2018; Lyra et al., 2018; Brandenburg and Oughton, 2018; Yang et al., 2018; Trivedi et al., 2018; Viviani et al., 2018; Bhatnagar et al., 2018b,a; Schreiber and Klahr, 2018; Bushby et al., 2018; Zhang and Yan, 2018; Bourdin and Brandenburg, 2018; Brandenburg et al., 2018b,a; Bourdin et al., 2018; Korsós et al., 2018; Rice and Nayakshin, 2018; Richert et al., 2018; Mitra et al., 2018; Brandenburg and Chatterjee, 2018; Kuchner et al., 2018; Perri and Brandenburg, 2018; Brandenburg, 2018),

31 times in 2017 (Bourdin, 2017; Yang et al., 2017; Bhat et al., 2017; Kahniashvili et al., 2017; Aarnes et al., 2017; Hollins et al., 2017; Reppin and Banerjee, 2017; Singh et al., 2017; Hord et al., 2017; Lyra et al., 2017; Baehr et al., 2017; Park, 2017; Sharma et al., 2017; Brandenburg and Kahniashvili, 2017; Käpylä et al., 2017a,b; Haugen et al., 2017; Gent et al., 2017; Osano and Adams, 2017; Cameron et al., 2017; Pekkilä et al., 2017; Brandenburg et al., 2017c,d,a,b,e; Aiyer et al., 2017; Li et al., 2017; Jabbari et al., 2017; Rempel et al., 2017; Smiet et al., 2017),

24 times in 2016 (Chatterjee et al., 2016; Chamandy, 2016; Chamandy et al., 2016; Candelaresi et al., 2016; Bhat et al., 2016a; Adams and Osano, 2016; Osano and Adams, 2016a,b; Krüger et al., 2016; Bhat et al., 2016b; Yang and Johansen, 2016; Cole et al., 2016; Kahniashvili et al., 2016; Warnecke et al., 2016; Jabbari et al., 2016; Lambrechts et al., 2016; Bourdin et al., 2016; Threlfall et al., 2016; Bhat and Brandenburg, 2016; Tian and Chen, 2016; Rodrigues et al., 2016; Lyra et al., 2016; Karak and Brandenburg, 2016; Yokoi and Brandenburg, 2016),

25 times in 2015 (Bourdin et al., 2015; Singh and Jingade, 2015; Jabbari et al., 2015; Jabbari, 2015; Chen et al., 2015; Johansen et al., 2015; Richert et al., 2015; Park and Park, 2015; Park, 2015; Smiet et al., 2015; Carrera et al., 2015; Gibbons et al., 2015; Baehr and Klahr, 2015; Snellman et al., 2015; Babkovskaia et al., 2015; Raettig et al., 2015; Andrievsky et al., 2015; Carrera et al., 2015; Chaudhuri, 2015; Singh et al., 2015; Lyra et al., 2015; Karak et al., 2015a,b; Brandenburg and Hubbard, 2015; Brandenburg et al., 2015),

37 times in 2014 (Bourdin, 2014; Bourdin et al., 2014; Carrera et al., 2014; Yang and Johansen, 2014a; Adams and Osano, 2014; Yang and Johansen, 2014b; Subramanian and Brandenburg, 2014; Singh et al., 2014; Jabbari and Brandenburg, 2014; Jabbari et al., 2014; Karak et al., 2014; Warnecke et al., 2014; McNally et al., 2014; Brandenburg et al., 2014; Gibbons et al., 2014; Pan and Padoan, 2014; Pan et al., 2014a,b; Lyra, 2014; Bhat et al., 2014; Losada et al., 2014; Rheinhardt et al., 2014; Mitra et al., 2014; Turner et al., 2014; Dittrich et al., 2014; Brandenburg and Stepanov, 2014; Chian et al., 2014; Brandenburg, 2014; Park, 2014b,a; Käpylä et al., 2014; Modestov et al., 2014; Cole et al., 2014; Rüdiger and Brandenburg, 2014; Warnecke and Brandenburg, 2014; Barekat and Brandenburg, 2014; Väisälä et al., 2014),

46 times in 2013 (Lyra and Kuchner, 2013; Bourdin et al., 2013a,b; Félix et al., 2013; Hubbard, 2013; Park et al., 2013; Park, 2013a,b; Getling, 2013; Devlen et al., 2013; Gent et al., 2013a,b; Brandenburg and Lazarian, 2013; Pan and Padoan, 2013; Mitra et al., 2013; van Wettum et al., 2013; Candelaresi and Brandenburg, 2013a,b; Kahniashvili et al., 2013; Lyra, 2013; Bhat and Subramanian, 2013; Raettig et al., 2013; Del Sordo et al., 2013; Chamandy et al., 2013; Di Bernardo and Torkelsson, 2013; Jabbari et al., 2013; Dittrich et al., 2013; Bingert and Peter, 2013; Brandenburg and Rädler, 2013; Bykov et al., 2013; Brandenburg, 2013; Warnecke et al., 2013a,b,c; Rempel et al., 2013; Mantere et al., 2013; Kemel et al., 2013a,b; Losada et al., 2013; Käpylä et al., 2013a,b,c; Svedin et al., 2013; Brandenburg et al., 2013a,b),

50 times in 2012 (Félix et al., 2012; Losada et al., 2012; Peter and Bingert, 2012; Lambrechts and Johansen, 2012; Kahniashvili et al., 2012; Tevzadze et al., 2012; Gent, 2012; Gibbons et al., 2012; Latter and Papaloizou, 2012; Hubbard, 2012; Gaburov et al., 2012; Yang and Krumholz, 2012; Lyra and Mac Low, 2012; McNally et al., 2012a,b; Bonanno et al., 2012; Haugen et al., 2012; Park and Blackman, 2012a,b; Mantere and Cole, 2012; Rogachevskii et al., 2012; Käpylä et al., 2012a,b; Maron et al., 2012; Horn et al., 2012; Lyra and Kuchner, 2012; Yang et al., 2012; Kitchatinov and Brandenburg, 2012; Brandenburg and Petrosyan, 2012; Hubbard and Brandenburg, 2012; Guerrero et al., 2012; Rice et al., 2012; Kemel et al., 2012a,b; Rheinhardt and Brandenburg, 2012; Peter et al., 2012; Brandenburg and Guerrero, 2012; Brandenburg et al., 2012a,b,c,d; Rempel et al., 2012; Del Sordo et al., 2012; Candelaresi and Brandenburg, 2012; Snellman et al., 2012a,b; Warnecke et al., 2012a,b,c; Johansen et al., 2012),

62 times in 2011 (Gastine and Dintrans, 2011a,b,c; Rice et al., 2011; Käpylä et al., 2011a,b,c; Mantere et al., 2011; Rogachevskii et al., 2011; Lambrechts, 2011; Johansen et al., 2011a,b; Rädler et al., 2011; Tarjei Jensen et al., 2011; Oishi and Mac Low, 2011; Ruoskanen et al., 2011; Fromang et al., 2011; Hydle Rivedal et al., 2011; Guerrero and Käpylä, 2011; Warnecke and Brandenburg, 2011b; Warnecke et al., 2011a,b; Kemel et al., 2011a,b,c; Bejarano et al., 2011; Zacharias et al., 2011a,b; Candelaresi and Brandenburg, 2011a,b; Candelaresi et al., 2011a,b,c; Del Sordo and Brandenburg, 2011a,b; Cantiello et al., 2011a,b; Rempel et al., 2011; Flock et al., 2011; Bingert and Peter, 2011; Käpylä and Korpi, 2011; Johansen et al., 2011c; Rüdiger et al., 2011; Lyra and Klahr, 2011; Mitra et al., 2011; Babkovskaia et al., 2011; Hubbard and Brandenburg, 2011; Chatterjee et al., 2011a,b,c; Chatterjee, 2011; Hubbard et al., 2011; Guerrero et al., 2011; Brandenburg and Nordlund, 2011; Warnecke and Brandenburg, 2011a; Brandenburg et al., 2011a,b,c; Brandenburg, 2011a,b,c,d),

30 times in 2010 (Haugen et al., 2010; Madarassy and Brandenburg, 2010; Gastine and Dintrans, 2010; Kahniashvili et al., 2010; Lyra et al., 2010; Johansen and Lacerda, 2010; Del Sordo et al., 2010; Fromang et al., 2010; Mitra et al., 2010a,b,c; Korpi et al., 2010; Käpylä et al., 2010a,b,c,d; Baggaley et al., 2010; Brandenburg and Dobler, 2010; Guerrero et al., 2010; Chatterjee et al., 2010; Rädler and Brandenburg, 2010; Bingert et al., 2010; Warnecke and Brandenburg, 2010; Hubbard and Brandenburg, 2010; Rheinhardt and Brandenburg, 2010; Brandenburg and Del Sordo, 2010; Brandenburg et al., 2010a,b; Brandenburg, 2010a,b),

35 times in 2009 (Yang et al., 2009; Baggaley et al., 2009; Rempel et al., 2009; Oishi and Mac Low, 2009; Snellman et al., 2009; Børve et al., 2009; Vermersch and Brandenburg, 2009; Heinemann and Papaloizou, 2009; Käpylä and Brandenburg, 2009; Johansen et al., 2009a,b; Maron and Mac Low, 2009; Zacharias et al., 2009a,b; Fromang et al., 2009; Mitra et al., 2009a,b; Käpylä et al., 2009a,b,c; Liljeström et al., 2009; Lyra et al., 2009a,b; Hubbard and Brandenburg, 2009; Sur and Brandenburg, 2009; Hubbard et al., 2009; Rädler and Brandenburg, 2009; Brandenburg et al., 2009a,b; Brandenburg, 2009a,b,c,d,e,f), 28 times in 2008 (Lyra et al., 2008a,b; Gastine and Dintrans, 2008a,b,c; Johansen and Levin,

2008; Workman and Armitage, 2008; Käpylä and Brandenburg, 2008; Klahr, 2008; Rieutord, 2008; Johansen et al., 2008; Yousef et al., 2008; Babkovskaia et al., 2008; Scharmer et al., 2008; Maron et al., 2008; Ruszkowski et al., 2008; Gellert et al., 2008; Rädler and Brandenburg, 2008; Tilgner and Brandenburg, 2008; Sur et al., 2008; Käpylä et al., 2008; Youdin and Johansen, 2008; Green et al., 2008; Brandenburg et al., 2008a,b,c; Brandenburg, 2008a,b),

19 times in 2007 (Käpylä and Brandenburg, 2007; Fromang et al., 2007; Fromang and Papaloizou, 2007; Oishi et al., 2007; Heinemann et al., 2007; Brandenburg and Käpylä, 2007; Schekochihin et al., 2007; Gustafsson et al., 2007; Ruszkowski et al., 2007; Johansen and Youdin, 2007; Youdin and Johansen, 2007; Johansen et al., 2007a,b; Sur et al., 2007; Brandenburg and Subramanian, 2007; Brandenburg et al., 2007a,b; Brandenburg, 2007a,b),

18 times in 2006 (Ouyed et al., 2006; Hupfer et al., 2006; Fromang et al., 2006; de Val-Borro et al., 2006; Haugen and Brandenburg, 2006; Johansen et al., 2006a,b,c; Shukurov et al., 2006; Mee and Brandenburg, 2006; Snodin et al., 2006; Brandenburg and Dintrans, 2006; Gustafsson et al., 2006; Heinemann et al., 2006; Dobler et al., 2006; Brandenburg, 2006a,b,c),

19 times in 2005 (Johansen and Klahr, 2005; McMillan and Sarson, 2005; Schekochihin et al., 2005; Dorch, 2005; Johansen et al., 2005; Christensson et al., 2005; Brandenburg and Rüdiger, 2005; Brandenburg and Blackman, 2005; Brandenburg and Käpylä, 2005; Brandenburg and Subramanian, 2005a,b,c; Brandenburg et al., 2005a,b; Brandenburg, 2005a; Brandenburg et al., 2005c; Brandenburg, 2005b,c,d),

19 times in 2004 (Nordlund, 2004; Brandenburg and Sandin, 2004; Brandenburg and Multamäki, 2004; Dorch, 2004a,b; Haugen and Brandenburg, 2004a,b; Haugen et al., 2004a,b,c; Yousef et al., 2004; Johansen et al., 2004; Maron et al., 2004; Pearson et al., 2004; Brandenburg and Matthaeus, 2004; Dobler and Getling, 2004; Brandenburg et al., 2004a,b,c),

and 7 times in 2003 (Yousef et al., 2003; Yousef and Brandenburg, 2003; McMillan and Sarson, 2003; Haugen et al., 2003; Brandenburg, 2003; Brandenburg et al., 2003; Dobler et al., 2003).

2 Papers by topic

The Pencil Code has been used for the following research topics

1. Interstellar and intercluster medium as well as early Universe

(a) Interstellar and intercluster medium (Candelaresi and Del Sordo, 2024; Korpi-Lagg et al., 2024; Elias-López et al., 2024, 2023; Pavaskar et al., 2023; Gent et al., 2023; Brandenburg and Ntormousi, 2022; Maiti et al., 2021; Gent et al., 2021; Li and Mattsson, 2021; Candelaresi and Del Sordo, 2020; Li and Mattsson, 2020; Brandenburg and Furuya, 2020; Brandenburg and Brüggen, 2020; Gent et al., 2020; Evirgen and Gent, 2019; Evirgen et al., 2019; Seta and Beck, 2019; Rodrigues et al., 2019; Brandenburg, 2019a; Väisälä et al., 2018; Zhang et al., 2018b; Zhang and Yan, 2018; Hollins et al., 2017; Hord et al., 2017; Chamandy, 2016; Chamandy et al., 2016; Rodrigues et al., 2016; Chamandy et al., 2013; Gent et al., 2013a,b; Bykov et al., 2013; Gent, 2012; Yang and Krumholz, 2012; Mantere and Cole, 2012; Rogachevskii et al., 2012; Ruoskanen et al., 2011; Ruszkowski et al., 2007, 2008; Brandenburg et al., 2007b; Gustafsson et al., 2006, 2007; Brandenburg et al., 2005a; Haugen et al., 2004b; Brandenburg et al., 2003).

(b) Small-scale dynamos and reconnection (Koshikumo et al., 2025; Kishore and Singh, 2025a; Brandenburg and Ntormousi, 2025; Warnecke et al., 2025; Gent et al., 2024; Zhou and Jingade, 2024; Qazi et al., 2025, 2024; Brandenburg and Larsson, 2023; Warnecke et al., 2023; Gent et al., 2022; Brandenburg et al., 2023c; Zhou et al., 2022; Bhat, 2021; Park and Cheoun, 2021; Santos-Lima et al., 2021; Park, 2020; Pusztai et al., 2020; Rüdiger et al., 2020; Seta et al., 2020; Käpylä, 2019; Bhat et al., 2019; Brandenburg and Rempel, 2019; Brandenburg et al., 2018a; Käpylä et al., 2018; Bhat et al., 2016b; Bhat and Subramanian, 2013; Brandenburg, 2011c; Baggaley et al., 2009, 2010; Schekochihin et al., 2005, 2007; Haugen and Brandenburg, 2004b; Haugen et al., 2003, 2004a,c; Dobler et al., 2003).

(c) Primordial magnetic fields and decaying turbulence (Dehman and Brandenburg, 2025; Vachaspati and Brandenburg, 2025; Brandenburg and Banerjee, 2024; Dwivedi et al., 2024; Brandenburg et al., 2024a, 2023d; Mtchedlidze et al., 2024, 2023, 2022; Bhat et al., 2021; Brandenburg, 2023a, 2020a; Brandenburg et al., 2020b, 2019b; Kahniashvili et al., 2020; Brandenburg et al., 2018b; Trivedi et al., 2018; Brandenburg et al., 2017d; Brandenburg and Kahniashvili, 2017; Kahniashvili et al., 2017; Reppin and Banerjee, 2017; Park, 2017; Osano and Adams, 2017; Adams and Osano, 2016; Osano and Adams, 2016b,a; Kahniashvili et al., 2016; Brandenburg et al., 2015; Adams and Osano, 2014; Kahniashvili et al., 2012, 2013; Tevzadze et al., 2012; Candelaresi and Brandenburg, 2011a; Kahniashvili et al., 2010; Del Sordo et al., 2010; Christensson et al., 2005; Yousef et al., 2004).

(d) Relic gravitational waves & axions (Iarygina et al., 2025; Sharma et al., 2025b; Brandenburg et al., 2024b,c; Iarygina et al., 2024; Sharma et al., 2023; He et al., 2023; Roper Pol, 2022; Sharma and Brandenburg, 2022; AlbertoRoper, 2022; Kahniashvili et al., 2022; Roper Pol, 2021; Roper Pol et al., 2022b; He et al., 2021b,a; Brandenburg et al., 2021b,d; Brandenburg and Sharma, 2021; Brandenburg et al., 2021a,c; Kahniashvili et al., 2021; Roper Pol et al., 2020b,a).

2. Planet formation and inertial particles

(a) Planet formation (Rice et al., 2025; Eriksson et al., 2025; Shi et al., 2025; Baehr et al., 2022; Yang and Zhu, 2021; Raettig et al., 2021; Baehr and Zhu, 2021b,a; Zhu and Yang, 2021; Klahr and Schreiber, 2021, 2020; Yang and Zhu, 2020; Eriksson et al., 2020; Gerbig et al., 2020; Castrejon et al., 2019; Baehr and Klahr, 2019; McNally et al., 2018; Schreiber and Klahr, 2018; Hernandez et al., 2019; Manser et al., 2019; Yang et al., 2018; Rice and Nayakshin, 2018; Richert et al., 2018; Kuchner et al., 2018; Baehr et al., 2017; Lyra et al., 2016; Yang and Johansen, 2016; Lambrechts et al., 2016; Johansen et al., 2015; Richert et al., 2015; Gibbons et al., 2015; Baehr and Klahr, 2015; Carrera et al., 2015, 2014; Yang and Johansen, 2014a,b; McNally et al., 2014; Turner et al., 2014; Gibbons et al., 2014; Dittrich et al., 2014, 2013; Hubbard, 2013; Lyra and Kuchner, 2013; Gibbons et al., 2012; Hubbard, 2012; Horn et al., 2012; Lyra and Kuchner, 2012; Yang et al., 2012; Lambrechts and Johansen, 2012; Johansen et al., 2012; Fromang et al., 2011; Johansen et al., 2011c; Lambrechts, 2011; Johansen et al., 2011a,b; Lyra and Klahr, 2011; Lyra et al., 2010; Johansen and Lacerda, 2010; Yang et al., 2009; Johansen et al., 2009b; Oishi and Mac Low, 2009; Børve et al., 2009; Lyra et al., 2009a,b, 2008a; Johansen et al., 2008; Lyra et al., 2008b; Youdin and Johansen, 2008; Oishi et al., 2007; Johansen et al., 2007a,b; Johansen and Youdin, 2007; Youdin and Johansen, 2007; Johansen et al., 2006a,b,c; Johansen and Klahr, 2005; Johansen et al., 2004, 2005).

(b) Inertial, tracer particles, & passive scalars (Saieed and Hickey, 2024; Kirchschlager et al., 2024; Sengupta and Umurhan, 2023; Li et al., 2022; Kirchschlager et al., 2021; Mattsson and Hedvall, 2021; Schaffer et al., 2021; Haugen et al., 2021a,b; Bhatnagar et al., 2021; Bhatnagar, 2020; Li et al., 2020; Mattsson et al., 2019a; Gerbig et al., 2019; Li et al., 2019; Aarnes et al., 2019b; Mattsson et al., 2019b; Hedvall and Mattsson, 2019; Lyra et al., 2018; Bhatnagar et al., 2018a; Schaffer et al., 2018; Mitra et al., 2018; Bhatnagar et al., 2018b; Yang et al., 2017; Aarnes et al., 2017; Sharma et al., 2017; Haugen et al., 2017; Li et al., 2017; Krüger et al., 2016; Raettig et al., 2015; Pan and Padoan, 2014, 2013; Pan et al., 2014b,a; Mitra et al., 2013; Haugen et al., 2012; Hydle Rivedal et al., 2011; Haugen et al., 2010).

3. Accretion discs and shear flows

(a) Accretion discs and shear flows (Godines et al., 2025; Meftah, 2025; Lyra et al., 2024; Sengupta et al., 2024; Cañas et al., 2024; Zhou, 2024; Mondal and Bhat, 2023; Meftah, 2023; Tharakkal et al., 2023a,b; Hyder et al., 2022, 2021, 2020; Bhat et al., 2017; Singh et al., 2017; Lyra et al., 2017; Bhat et al., 2016a; Tian and Chen, 2016; Lyra, 2014; Lyra et al., 2015; Väisälä et al., 2014; Lyra, 2013; Raettig et al., 2013; Di Bernardo and Torkelsson, 2013; Latter and Papaloizou, 2012; Gaburov et al., 2012; Lyra and Mac Low, 2012; Rice et al., 2011, 2012; Oishi and Mac Low, 2011; Flock et al., 2011; Käpylä et al., 2010a; Käpylä and Korpi, 2011; Fromang et al., 2010; Korpi et al., 2010; Johansen et al., 2009a; Heinemann and Papaloizou, 2009; Fromang et al., 2009; Johansen and Levin, 2008; Workman and Armitage, 2008; Fromang et al., 2007; Fromang and Papaloizou, 2007; Ouyed et al., 2006; Brandenburg, 2005d).

(b) Shear flows (Barekat et al., 2020; Singh and Jingade, 2015; Modestov et al., 2014; Vermersch and Brandenburg, 2009; Käpylä et al., 2009c; Green et al., 2008; Yousef et al., 2008; Babkovskaia et al., 2008; Brandenburg et al., 2004a).

4. Solar physics (a) Coronal heating and coronal mass ejections (Srivastava et al., 2025; Kishore and Singh,

2025a,b; Singh et al., 2025; Vemareddy, 2024; Kesri et al., 2024; Maity et al., 2024b; Dey et al., 2024; Vemareddy et al., 2024; Zhang et al., 2023; Dey et al., 2022; Chatterjee and Dey, 2022; Jakab and Brandenburg, 2021; Zhuleku et al., 2021; Adrover-González and Terradas, 2020; Bourdin, 2014, 2017, 2020; Bourdin et al., 2013a,b, 2014, 2015, 2016; Chatterjee, 2020; Warnecke and Bingert, 2020; Candelaresi et al., 2019; Warnecke and Peter, 2019b; Smiet et al., 2019; Warnecke and Peter, 2019a; Korsós et al., 2018; Cameron et al., 2017; Chatterjee et al., 2016; Candelaresi et al., 2016; Threlfall et al., 2016; Chen et al., 2015; Smiet et al., 2015; Warnecke and Brandenburg, 2014; van Wettum et al., 2013; Bingert and Peter, 2013; Peter and Bingert, 2012; Peter et al., 2012; Warnecke et al., 2012a,b; Warnecke and Brandenburg, 2011a; Zacharias et al., 2011a,b; Warnecke et al., 2011b; Bingert and Peter, 2011; Warnecke and Brandenburg, 2011b; Warnecke et al., 2011a; Warnecke and Brandenburg, 2010; Bingert et al., 2010; Zacharias et al., 2009b,a).

(b) Large-scale dynamos, helical turbulence, and catastrophic quenching (Shchutskyi et al., 2025; Brandenburg et al., 2025b; Brandenburg and Vishniac, 2025; Rogachevskii et al., 2025; Brandenburg et al., 2025a; Mondal et al., 2025; Hidalgo et al., 2025; Zhou and Lai, 2024; Vashishth, 2024; Zhou and Blackman, 2024; Zhu and Shi, 2023; Park et al., 2023; Yang and Zhu, 2022; Prabhu et al., 2021; Brandenburg and Scannapieco, 2020; Park, 2019a; Peng et al., 2019; Nauman and Nättilä, 2019; Park, 2019b; Brandenburg and Oughton, 2018; Bourdin et al., 2018; Bourdin and Brandenburg, 2018; Brandenburg, 2018; Brandenburg and Chatterjee, 2018; Rempel et al., 2019; Brandenburg et al., 2017a,c,b; Rempel et al., 2017; Smiet et al., 2017; Cole et al., 2016; Karak and Brandenburg, 2016; Karak et al., 2015b; Brandenburg and Hubbard, 2015; Subramanian and Brandenburg, 2014; Brandenburg and Stepanov, 2014; Brandenburg, 2014; Bhat et al., 2014; Chian et al., 2014; Park, 2014b; Park et al., 2013; Brandenburg and Lazarian, 2013; Park, 2013b,a, 2014a; Candelaresi and Brandenburg, 2013a; Park, 2013a; Del Sordo et al., 2013; Brandenburg, 2013; Rempel et al., 2013; Candelaresi and Brandenburg, 2013b, 2012; Brandenburg et al., 2012d; Rempel et al., 2012; Park and Blackman, 2012b,a; Brandenburg and Guerrero, 2012; Brandenburg, 2011a; Hubbard and Brandenburg, 2012; Rempel et al., 2011; Mitra et al., 2011; Candelaresi et al., 2011b; Hubbard and Brandenburg, 2011; Brandenburg, 2011b; Chatterjee et al., 2011a; Hubbard et al., 2011; Candelaresi et al., 2011c; Candelaresi and Brandenburg, 2011b; Candelaresi et al., 2011a; Brandenburg, 2011d; Guerrero et al., 2011; Hubbard and Brandenburg, 2010; Mitra et al., 2010a,b; Brandenburg, 2010b; Guerrero et al., 2010; Brandenburg, 2010a; Brandenburg et al., 2010a; Chatterjee et al., 2010; Rädler and Brandenburg, 2010; Rempel et al., 2009; Käpylä and Brandenburg, 2009; Brandenburg, 2009a,e; Brandenburg et al., 2009a; Brandenburg, 2009d,f; Sur and Brandenburg, 2009; Brandenburg, 2009b,c; Rädler and Brandenburg, 2008; Tilgner and Brandenburg, 2008; Brandenburg, 2008a; Brandenburg et al., 2008c; Brandenburg, 2008b; Brandenburg and Käpylä, 2007; Brandenburg and Subramanian, 2007; Brandenburg, 2007b,a, 2006c,b; Shukurov et al., 2006; Mee and Brandenburg, 2006; Snodin et al., 2006; Brandenburg and Dintrans, 2006; Brandenburg, 2006a; Brandenburg et al., 2005b; Brandenburg and Subramanian, 2005c,b; Brandenburg and Käpylä, 2005; Brandenburg, 2005a; Brandenburg and Blackman, 2005; Brandenburg and Subramanian, 2005a; Brandenburg, 2005b,c; Brandenburg et al., 2004c; Brandenburg and Matthaeus, 2004; Brandenburg and Sandin, 2004; Yousef and Brandenburg, 2003).

(c) Helioseismology (Kishore et al., 2024; Singh et al., 2014, 2015, 2020).

(d) Strongly stratified MHD turbulence and NEMPI (Losada et al., 2019; Perri and Brandenburg, 2018; Jabbari et al., 2017, 2016; Warnecke et al., 2016; Jabbari, 2015; Brandenburg et al., 2014; Losada et al., 2014; Mitra et al., 2014; Jabbari and Brandenburg, 2014; Jabbari et al., 2014, 2015; Brandenburg et al., 2013b; Warnecke et al., 2013c; Jabbari et al., 2013; Kemel et al., 2013a,b, 2012a,b, 2011a,b,c; Losada et al., 2013; Käpylä et al., 2013a; Losada et al., 2012; Käpylä et al., 2012a; Brandenburg et al., 2010b, 2011c, 2012a; Rüdiger et al., 2011).

(e) Convection in Cartesian domains (Käpylä, 2025; Pandey and Bourdin, 2025; Hosking et al., 2025; Käpylä, 2024, 2023b; Ortiz-Rodríguez et al., 2023; Tschernitz and Bourdin, 2022, 2025; Masada and Sano, 2022; Ortiz-Rodríguez et al., 2022; Käpylä, 2022, 2021a; Brandenburg et al., 2019a; Käpylä, 2018; Bushby et al., 2018; Käpylä et al., 2017b; Félix et al., 2013; Käpylä et al., 2013b; Getling, 2013; Félix et al., 2012; Svedin et al., 2013; Guerrero et al., 2012; Gastine and Dintrans, 2011c; Mantere et al., 2011; Käpylä et al., 2011c; Guerrero and Käpylä, 2011; Cantiello et al., 2011a,b; Gastine and Dintrans, 2008a,b, 2010, 2011a,b; Brandenburg et al., 2011b; Käpylä et al., 2008, 2009b, 2010b; Scharmer et al., 2008; Rieutord, 2008; Heinemann et al., 2007, 2006; Nordlund, 2004; Dobler and Getling, 2004).

(f) Global convection and dynamo simulations (Hidalgo et al., 2024; Hackman et al., 2024; Käpylä et al., 2023; Karak, 2023; Hidalgo et al., 2023; Käpylä, 2023a; Stejko et al., 2022a,b; Warnecke et al., 2021; Käpylä, 2021b; Navarrete et al., 2023, 2022, 2021, 2020; Becerra et al., 2022a,b, 2021; Viviani et al., 2021; Viviani and Käpylä, 2021; Willamo et al., 2020; Jakab and Brandenburg, 2020; Käpylä et al., 2020b; Viviani et al., 2019; Rüdiger et al., 2019; Käpylä et al., 2019; Warnecke, 2018; Viviani et al., 2018; Käpylä et al., 2017a; Gent et al., 2017; Karak et al., 2015a; Warnecke et al., 2014; Cole et al., 2014; Käpylä et al., 2010d, 2011a,b, 2012b, 2013c, 2014; Mantere et al., 2013; Warnecke et al., 2012c, 2013a,b; Mitra et al., 2009b, 2010c; Brandenburg et al., 2007a; Dobler et al., 2006; McMillan and Sarson, 2005; Dorch, 2004a,b, 2005; McMillan and Sarson, 2003).

5. Miscellanea

(a) Turbulent transport and test-field method (Candelaresi and Beck, 2023; Brandenburg and Protiti, 2023; Mizerski et al., 2023; Carenza et al., 2023; Käpylä and Singh, 2022; Käpylä et al., 2022; Zhou and Blackman, 2021; Haugen et al., 2021a; Käpylä et al., 2020a; Brandenburg and Chen, 2020; Peng et al., 2019; Warnecke et al., 2018; Andrievsky et al., 2015; Snellman et al., 2015; Karak et al., 2014; Rheinhardt et al., 2014; Rüdiger and Brandenburg, 2014; Devlen et al., 2013; Brandenburg et al., 2004b, 2008a,b, 2009b, 2012b,c, 2013a; Brandenburg and Rädler, 2013; Snellman et al., 2009, 2012a,b; Kitchatinov and Brandenburg, 2012; Rheinhardt and Brandenburg, 2010, 2012; Rogachevskii et al., 2011; Rädler et al., 2011; Chatterjee, 2011; Brandenburg and Del Sordo, 2010; Madarassy and Brandenburg, 2010; Käpylä et al., 2010c; Hubbard and Brandenburg, 2009; Hubbard et al., 2009; Rädler and Brandenburg, 2009; Käpylä et al., 2009a; Mitra et al., 2009a; Liljeström et al., 2009; Sur et al., 2008; Käpylä and Brandenburg, 2007, 2008; Sur et al., 2007; Hupfer et al., 2006; Yousef et al., 2003).

(b) Hydrodynamic and MHD instabilities (Oliveira et al., 2021; Del Sordo et al., 2012; Chatterjee et al., 2011b,c; Bejarano et al., 2011; Brandenburg and Rüdiger, 2005; Brandenburg et al., 2004c; Brandenburg, 2003).

(c) Chiral MHD (Schober et al., 2024b,a; Brandenburg et al., 2023a,b; Schober et al., 2022a,b, 2020a,b, 2019, 2018; Brandenburg et al., 2017e).

(d) Hydrodynamic and MHD turbulence (Brandenburg and Scannapieco, 2025; Park, 2025; Roper Pol and Salvino Midiri, 2025; Brandenburg et al., 2025c, 2023e; Brandenburg and Boldyrev, 2020; Aiyer et al., 2017; Yokoi and Brandenburg, 2016; Brandenburg and Petrosyan, 2012; Del Sordo and Brandenburg, 2011a,b; Brandenburg and Nordlund, 2011; Haugen and Brandenburg, 2004a, 2006; Brandenburg et al., 2005c; Pearson et al., 2004).

(e) Turbulent combustion, front propagation, radiation & ionization (Sabelnikov et al., 2025; Yuvraj et al., 2025; Lipatnikov, 2024b; Wang et al., 2024; Ganti et al., 2023; Yuvraj et al., 2023; Lipatnikov and Sabelnikov, 2022, 2023; Karchniwy et al., 2022; Bhatia and De, 2021; Zhang et al., 2020; Aarnes et al., 2020; Brandenburg and Das, 2021, 2020; Qian et al., 2020; Brandenburg, 2023b, 2020b, 2019b; Mao et al., 2019; Bhat and Brandenburg, 2016; Babkovskaia et al., 2015; Chaudhuri, 2015; Barekat and Brandenburg, 2014; Tarjei Jensen et al., 2011; Brandenburg et al., 2011a; Babkovskaia et al., 2011; Brandenburg and Multamäki, 2004).

(f) Code development, GPU etc (Lyra, 2023; Pencil Code Collaboration et al., 2021; Pekkilä et al., 2022, 2017).

3 Code comparison & reference

The Pencil Code has been quoted in other papers either for detailed code comparison, in connection with related work, or in comparison with other codes (Lebreuilly et al., 2025; Abramson et al., 2025; Hunana, 2025; Lebreuilly et al., 2025; Irshad P et al., 2025; Son et al., 2025; Sharma et al., 2025a; Yeung et al., 2025; Zhou et al., 2025; Lim et al., 2025; Schad et al., 2024; Achikanath Chirakkara et al., 2024; Raboonik et al., 2024; Figueroa et al., 2024; Rea et al., 2024; Shariff, 2024; Sandnes et al., 2024; Dahl et al., 2024; Hunana, 2024; Shi et al., 2024; Owens and Wadsley, 2024; Modestov et al., 2024; Rasheed et al., 2023; Modestov et al., 2023; Väisälä et al., 2023; Lecoanet and Edelmann, 2023; Lesur et al., 2023; Klahr et al., 2023; Ruszkowski and Pfrommer, 2023; Commerçon et al., 2023; Paardekooper et al., 2022; Chouliaras and Gourgouliatos, 2022; Caldwell et al., 2022; Porter et al., 2022; Li and Youdin, 2021; Zhu, 2021; Sabelnikov et al., 2021; Bartman et al., 2021; Hanawa and Matsumoto, 2021; Bhatia and De, 2021; Väisälä et al., 2021; Brandenburg, 2020c; Pencil Code Collaboration, 2020; Guerrero, 2020; Gressel and Elstner, 2020; Matilsky and Toomre, 2020; Brandenburg et al., 2020a; Rosswog, 2020; Beresnyak, 2019; Sapetina et al., 2019; Rosswog, 2019; Mignone et al., 2019; Tricco, 2019; Jóhannesson et al., 2019; Porter et al., 2019; Zhang et al., 2018a; Li et al., 2018a; Nixon et al., 2018; Rüdiger et al., 2018; Hernandez et al., 2018; Oishi et al., 2018; Augustson, 2017b; Yamamoto and Makino, 2017; Goffrey et al., 2017; Augustson, 2017a; Ryu and Huynh, 2017; Cabezón et al., 2017; Emeriau-Viard and Brun, 2017; Brun and Browning, 2017; Kupka and Muthsam, 2017; Kulikov et al., 2016; Surville et al., 2016; Simon et al., 2016; Skála et al., 2015; Mocz et al., 2015; Hopkins, 2015; Duffell and MacFadyen, 2015; Krumholz and Forbes, 2015; Cheung et al., 2015; Augustson et al., 2015; Schad et al., 2015; Brun et al., 2015; Norton et al., 2014; Rieutord, 2014; Olshevsky et al., 2014; Skála et al., 2014; Jenkins et al., 2014; Lovelace and Romanova, 2014; Recchi, 2014; Berera and Linkmann, 2014; Norton et al., 2014; Charbonneau, 2014, 2013; Augustson et al., 2013; Gabbasov et al., 2013; Kulikov, 2013; Fromang, 2013; Martínez Pillet, 2013; Cavecchi et al., 2013; Rein, 2012; Freytag et al., 2012; McNally et al., 2012a; Bonanno et al., 2012; Maron et al., 2012; McNally et al., 2012b; Andic, 2011; Viallet et al., 2011; McNally, 2011; Vshivkov et al., 2011; Ziegler, 2011; Hanasz et al., 2010; Brandenburg and Dobler, 2010; Rovithis-Livaniou, 2010; Bai and Stone, 2010; Stone and Gardiner, 2010; Turck-Chièze, 2010; Garcia de Andrade, 2009; Kley, 2009; Piontek et al., 2009; Maron and Mac Low, 2009; Hawley, 2009; Lemaster and Stone, 2009; Matsumoto and Seki, 2008; Maron et al., 2008; Gellert et al., 2008; Klahr, 2008; Thévenin et al., 2006; Fromang et al., 2006; de Val-Borro et al., 2006; Turner et al., 2006; Rüdiger, 2005; Maron et al., 2004).

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Bourdin, P.A., Bingert, S. and Peter, H., Observationally driven 3D magnetohydrodynamics model of the solar corona above an active region. Astron. Astrophys., 2013a, 555, A123.

Bourdin, P.A., Bingert, S. and Peter, H., VizieR Online Data Catalog: 3D-MHD model of a solar active region corona. VizieR Online Data Catalog, 2013b, 355.

Bourdin, P.A., Bingert, S. and Peter, H., Scaling laws of coronal loops compared to a 3D MHD model of an active region. Astron. Astrophys., 2016, 589, A86.

Bourdin, P.A., Plasma Beta Stratification in the Solar Atmosphere: A Possible Explanation for the Penumbra Formation. Astrophys. J. Lett., 2017, 850, L29.

Bourdin, P.A., Bingert, S. and Peter, H., Coronal energy input and dissipation in a solar active region 3D MHD model. Astron. Astrophys., 2015, 580, A72.

Bourdin, P., Singh, N.K. and Brandenburg, A., Magnetic Helicity Reversal in the Corona at Small Plasma Beta. Astrophys. J., 2018, 869, 2.

Bourdin, P.A., Driving solar coronal MHD simulations on highperformance computers. Geophys. Astrophys. Fluid Dynam., 2020, 114, 235–260.

Bourdin, P.A., Bingert, S. and Peter, H., Coronal loops above an active region: Observation versus model. Pub. Astron. Soc. Japan, 2014, 66, S7.

Bourdin, P.A. and Brandenburg, A., Magnetic Helicity from Multipolar Regions on the Solar Surface. Astrophys. J., 2018, 869, 3.

Brandenburg, A., Computational aspects of astrophysical MHD and turbulence; in Advances in Nonlinear Dynamos. Series: The Fluid Mechanics of Astrophysics and Geophysics, edited by A. Ferriz-Mas and M. Núñez, ISBN: 978-0-415-28788-3. CRC Press, Apr., 2003, pp. 269–344.

Brandenburg, A., Distributed versus tachocline dynamosa; in Solar activity: exploration, understanding and prediction, edited by H. Lundstedt, ESA, ESTEC Noordwijk, The Netherlands, Dec., 2005a.

Brandenburg, A., Importance of Magnetic Helicity in Dynamosb; in Cosmic Magnetic Fields, edited by R. Wielebinski and R. Beck, Vol. 664 of Lecture Notes in Physics, Berlin Springer Verlag, 2005b, p. 219.

Brandenburg, A., The Case for a Distributed Solar Dynamo Shaped by Near-Surface Shear. Astrophys. J., 2005c, 625, 539– 547.

Brandenburg, A., Turbulence and its parameterization in accretion discs. Astron. Nachr., 2005d, 326, 787–797.

Brandenburg, A., Location of the Solar Dynamo and Near-Surface Sheara; in Solar MHD Theory and Observations: A High Spatial Resolution Perspective, edited by J. Leibacher, R.F. Stein and H. Uitenbroek, Vol. 354 of Astron. Soc. Pac. Conf. Ser., Dec., 2006a, p. 121.

Brandenburg, A., Magnetic helicity in primordial and dynamo scenarios of galaxies. Astron. Nachr., 2006b, 327, 461.

Brandenburg, A., Why coronal mass ejections are necessary for the dynamoc; in IAU Joint Discussion, Vol. 8 of IAU Joint Discussion, Aug., 2006c.

Brandenburg, A., Near-surface shear layer dynamicsa; in IAU Symp., edited by F. Kupka, I. Roxburgh and K.L. Chan, Vol. 239 of IAU Symp., May, 2007a, pp. 457–466.

Brandenburg, A., Why coronal mass ejections are necessary for the dynamo. Highlights Astron., 2007b, 14, 291–292.

Brandenburg, A., The dual role of shear in large-scale dynamos. Astron. Nachr., 2008a, 329, 725.

Brandenburg, A., Turbulent protostellar discs. Phys. Scripta Vol. T, 2008b, 130, 014016.

Brandenburg, A., Advances in Theory and Simulations of Large-Scale Dynamos. Space Sci. Ref., 2009a, 144, 87–104.

Brandenburg, A., Advances in Theory and Simulations of Large-Scale Dynamosb; in The Origin and Dynamics of Solar Magnetism, Space Sciences Series of ISSI, Volume 32. ISBN 978-1-4419-0238-2. Springer New York, 2009, p. 87, edited by M.J. Thompson, A. Balogh, J.L. Culhane, Å. Nordlund, S.K. Solanki and J.P. Zahn, Springer New York, 2009b, p. 87.

Brandenburg, A., From Fibril to Diffuse Fields During Dynamo Saturationc; in Solar-Stellar Dynamos as Revealed by Helioand Asteroseismology: GONG 2008/SOHO 21, edited by M. Dikpati, T. Arentoft, I. González Hernández, C. Lindsey and F. Hill, Vol. 416 of Astron. Soc. Pac. Conf. Ser., Dec., 2009c, p. 433.

Brandenburg, A., Large-scale Dynamos at Low Magnetic Prandtl Numbers. Astrophys. J., 2009d, 697, 1206–1213.

Brandenburg, A., Paradigm shifts in solar dynamo modelinge; in IAU Symp., edited by K.G. Strassmeier, A.G. Kosovichev and J.E. Beckman, Vol. 259 of IAU Symp., Apr., 2009e, pp. 159– 166.

Brandenburg, A., The critical role of magnetic helicity in astrophysical large-scale dynamos. Plasma Phys. Contr. Fusion, 2009f, 51, 124043.

Brandenburg, A., Magnetic field evolution in simulations with Euler potentials. Month. Not. Roy. Astron. Soc., 2010a, 401, 347– 354.

Brandenburg, A., Surface appearance of dynamo-generated largescale fieldsb; in 38th COSPAR Scientific Assembly, Vol. 38 of COSPAR Meeting, 2010b, p. 2826.

Brandenburg, A., Chandrasekhar-Kendall functions in astrophysical dynamos. Pramana, 2011a, 77, 67–76.

Brandenburg, A., Dissipation in dynamos at low and high magnetic Prandtl numbers. Astron. Nachr., 2011b, 332, 51.

Brandenburg, A., Nonlinear Small-scale Dynamos at Low Magnetic Prandtl Numbers. Astrophys. J., 2011c, 741, 92.

Brandenburg, A., Simulations of astrophysical dynamosd; in IAU Symp., edited by A. Bonanno, E. de Gouveia Dal Pino and A.G. Kosovichev, Vol. 274 of IAU Symp., Jun., 2011d, pp. 402–409.

Brandenburg, A., Non-linear and chaotic dynamo regimes; in IAU Symp., edited by A.G. Kosovichev, E. de Gouveia Dal Pino and Y. Yan, Vol. 294 of IAU Symp., Jul., 2013, pp. 387–398.

Brandenburg, A., Magnetic Prandtl Number Dependence of the Kinetic-to-magnetic Dissipation Ratio. Astrophys. J., 2014, 791, 12.

Brandenburg, A. and Banerjee, A., Turbulent magnetic decay controlled by two conserved quantities. J. Plasma Phys., 2025, 91, E5.

Brandenburg, A. and Blackman, E.G., Ejection of Bi-Helical Fields from the Sun. Highlights Astron., 2005, 13, 101.

Brandenburg, A., Candelaresi, S. and Chatterjee, P., Small-scale magnetic helicity losses from a mean-field dynamo. Month. Not. Roy. Astron. Soc., 2009a, 398, 1414–1422.

Brandenburg, A., Candelaresi, S. and Gent, F.A., Introduction to The Physics and Algorithms of the Pencil Code. Geophys. Astrophys. Fluid Dynam., 2020a, 114, 1–7.

Brandenburg, A. and Chatterjee, P., Strong nonlocality variations in a spherical mean-field dynamo. Astronomische Nachrichten, 2018, 339, 118–126.

Brandenburg, A., Chatterjee, P., Del Sordo, F., Hubbard, A., Käpylä, P.J. and Rheinhardt, M., Turbulent transport in hydromagnetic flows. Phys. Scripta Vol. T, 2010a, 142, 014028.

Brandenburg, A. and Del Sordo, F., Turbulent diffusion and galactic magnetism. Highlights Astron., 2010, 15, 432–433.

Brandenburg, A. and Dintrans, B., Nonaxisymmetric stability in the shearing sheet approximation. Astron. Astrophys., 2006, 450, 437–444.

Brandenburg, A., Dintrans, B. and Haugen, N.E.L., Shearing and embedding box simulations of the magnetorotational instabilitya; in MHD Couette Flows: Experiments and Models, edited by R. Rosner, G. Rüdiger and A. Bonanno, Vol. 733 of Am. Inst. Phys. Conf. Ser., Nov., 2004a, pp. 122–136.

Brandenburg, A. and Dobler, W., Pencil Code: Finite-difference Code for Compressible Hydrodynamic Flows, Astrophysics Source Code Library 2010.

Brandenburg, A., Gressel, O., Jabbari, S., Kleeorin, N. and Rogachevskii, I., Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field. Astron. Astrophys., 2014, 562, A53.

Brandenburg, A., Gressel, O., Käpylä, P.J., Kleeorin, N., Mantere, M.J. and Rogachevskii, I., New scaling for the alpha effect in slowly rotating turbulence. Astrophys. J., 2013a, 762, 127.

Brandenburg, A. and Guerrero, G., Cycles and cycle modulations; in IAU Symp., edited by C.H. Mandrini and D.F. Webb, Vol. 286 of IAU Symp., Jul., 2012, pp. 37–48.

Brandenburg, A., Haugen, N. and Mee, A., Nonhelical turbulent dynamos: shocks and sheara; in The Magnetized Plasma in Galaxy Evolution, edited by K.T. Chyzy, K. Otmianowska-Mazur, M. Soida and R.J. Dettmar, Jun., 2005a, pp. 139–146.

Brandenburg, A., Haugen, N.E.L. and Babkovskaia, N., Turbulent front speed in the Fisher equation: Dependence on Damköhler number. Phys. Rev. E, 2011a, 83, 016304.

Brandenburg, A., Haugen, N.E.L. and Dobler, W., MHD simulations of small and large scale dynamos; in Turbulence, Waves, and Instabilities in the Solar Plasma, ed. R. Erdélyi, K. Petrovay, B. Roberts, & M. Aschwanden, edited by R. Erdélyi, K. Petrovay, B. Roberts and M. Aschwanden, Kluwer Acad. Publ., Dordrecht, Mar., 2003, pp. 33–53.

Brandenburg, A., Haugen, N.E.L., Käpylä, P.J. and Sandin, C., The problem of small and large scale fields in the solar dynamo. Astron. Nachr., 2005b, 326, 174–185.

Brandenburg, A., Haugen, N.E.L., Li, X.Y. and Subramanian, K., Varying the forcing scale in low Prandtl number dynamos. Month. Not. Roy. Astron. Soc., 2018a, 479, 2827–2833.

Brandenburg, A. and Hubbard, P. J., A.K., Dynamical quenching with non-local α and downward pumping. Astron. Nachr., 2015, 336, 91–96.

Brandenburg, A. and Kahniashvili, T., Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay. Phys. Rev. Lett., 2017, 118, 055102.

Brandenburg, A., Kahniashvili, T. and Tevzadze, A.G., Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field. Phys. Rev. Lett., 2015, 114, 075001.

Brandenburg, A., Käpylä, P. and Mohammed, A., Passive scalar diffusion as a damped wavec; in Progress in Turbulence, edited by J. Peinke, A. Kittel, S. Barth and M. Oberlack, Springer-Verlag, Apr., 2005c, pp. 3–6.

Brandenburg, A. and Käpylä, P.J., Connection between active longitudes and magnetic helicity. astro-ph/0512639, 2005.

Brandenburg, A. and Käpylä, P.J., Magnetic helicity effects in astrophysical and laboratory dynamos. New J. Phys., 2007, 9, 305.

Brandenburg, A., Käpylä, P.J. and Korpi, M.J., From convective to stellar dynamosb; in IAU Symp., edited by N.H. Brummell, A.S. Brun, M.S. Miesch and Y. Ponty, Vol. 271 of IAU Symp., Aug., 2011b, pp. 279–287.

Brandenburg, A., Käpylä, P.J., Mitra, D., Moss, D. and Tavakol, R., The helicity constraint in spherical shell dynamos. Astron. Nachr., 2007a, 328, 1118.

Brandenburg, A., Käpylä, P.J. and Mohammed, A., Non-Fickian diffusion and tau approximation from numerical turbulence. Phys. Fluids, 2004b, 16, 1020–1027.

Brandenburg, A., Kemel, K., Kleeorin, N., Mitra, D. and Rogachevskii, I., Detection of Negative Effective Magnetic Pressure Instability in Turbulence Simulations. Astrophys. J. Lett., 2011c, 740, L50.

Brandenburg, A., Kemel, K., Kleeorin, N. and Rogachevskii, I., The Negative Effective Magnetic Pressure in Stratified Forced Turbulence. Astrophys. J., 2012a, 749, 179.

Brandenburg, A., Kleeorin, N. and Rogachevskii, I., Large-scale magnetic flux concentrations from turbulent stresses. Astron. Nachr., 2010b, 331, 5.

Brandenburg, A., Kleeorin, N. and Rogachevskii, I., Self-assembly of Shallow Magnetic Spots through Strongly Stratified Turbulence. Astrophys. J. Lett., 2013b, 776, L23.

Brandenburg, A., Korpi, M.J. and Mee, A.J., Thermal Instability in Shearing and Periodic Turbulence. Astrophys. J., 2007b, 654, 945–954.

Brandenburg, A. and Lazarian, A., Astrophysical Hydromagnetic Turbulence. Space Sci. Ref., 2013, 178, 163–200.

Brandenburg, A. and Matthaeus, W.H., Magnetic helicity evolution in a periodic domain with imposed field. Phys. Rev. E, 2004, 69, 056407.

Brandenburg, A. and Multamäki, T., How long can left and right handed life forms coexist?. Int. J. Astrobiology, 2004, 3, 209– 219.

Brandenburg, A., Neronov, A. and Vazza, F., Resistively controlled primordial magnetic turbulence decay. Astron. Astrophys., 2024a, 687, A186.

Brandenburg, A. and Nordlund, Å., Astrophysical turbulence modeling. Rep. Progr. Phys., 2011, 74, 046901.

Brandenburg, A. and Oughton, S., Cross-helically forced and decaying hydromagnetic turbulence. Astronomische Nachrichten, 2018, 339, 641–646.

Brandenburg, A., Petrie, G.J.D. and Singh, N.K., Two-scale Analysis of Solar Magnetic Helicity. Astrophys. J., 2017a, 836, 21.

Brandenburg, A. and Petrosyan, A., Kinetic helicity decay in linearly forced turbulence. Astron. Nachr., 2012, 333, 195.

Brandenburg, A. and Rädler, K.H., Yoshizawa’s cross-helicity effect and its quenching. Geophys. Astrophys. Fluid Dynam., 2013, 107, 207–217.

Brandenburg, A., Rädler, K.H. and Kemel, K., Mean-field transport in stratified and/or rotating turbulence. Astron. Astrophys., 2012b, 539, A35.

Brandenburg, A., Rädler, K.H. and Kemel, K., Mean-field transport in stratified and/or rotating turbulence (Corrigendum). Astron. Astrophys., 2012c, 545, C1.

Brandenburg, A., Rädler, K.H., Rheinhardt, M. and Käpylä, P.J., Magnetic Diffusivity Tensor and Dynamo Effects in Rotating and Shearing Turbulence. Astrophys. J., 2008a, 676, 740–751.

Brandenburg, A., Rädler, K.H., Rheinhardt, M. and Subramanian, K., Magnetic Quenching of α and Diffusivity Tensors in Helical Turbulence. Astrophys. J. Lett., 2008b, 687, L49–L52.

Brandenburg, A., Rädler, K.H. and Schrinner, M., Scale dependence of alpha effect and turbulent diffusivity. Astron. Astrophys., 2008c, 482, 739–746.

Brandenburg, A. and Rüdiger, G., The angular momentum transport by the strato-rotational instability in simulated Taylor-Couette flows. astro-ph/0512409, 2005.

Brandenburg, A. and Sandin, C., Catastrophic alpha quenching alleviated by helicity flux and shear. Astron. Astrophys., 2004, 427, 13–21.

Brandenburg, A., Sandin, C. and Käpylä, P.J., Helical coronal ejections and their role in the solar cyclec; in Multi-Wavelength Investigations of Solar Activity, edited by A.V. Stepanov, E.E. Benevolenskaya and A.G. Kosovichev, Vol. 223 of IAU Symp., 2004c, pp. 57–64.

Brandenburg, A., Schober, J. and Rogachevskii, I., The contribution of kinetic helicity to turbulent magnetic diffusivity. Astronomische Nachrichten, 2017b, 338, 790–793.

Brandenburg, A., Sokoloff, D. and Subramanian, K., Current Status of Turbulent Dynamo Theory. From Large-Scale to Small-Scale Dynamos. Space Sci. Ref., 2012d, 169, 123–157.

Brandenburg, A. and Stepanov, R., Faraday Signature of Magnetic Helicity from Reduced Depolarization. Astrophys. J., 2014, 786, 91.

Brandenburg, A. and Subramanian, K., Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep., 2005a, 417, 1–209.

Brandenburg, A. and Subramanian, K., Minimal tau approximation and simulations of the alpha effect. Astron. Astrophys., 2005b, 439, 835–843.

Brandenburg, A. and Subramanian, K., Strong mean field dynamos require supercritical helicity fluxes. Astron. Nachr., 2005c, 326, 400–408.

Brandenburg, A. and Subramanian, K., Simulations of the anisotropic kinetic and magnetic alpha effects. Astron. Nachr., 2007, 328, 507.

Brandenburg, A., Svedin, A. and Vasil, G.M., Turbulent diffusion with rotation or magnetic fields. Month. Not. Roy. Astron. Soc., 2009b, 395, 1599–1606.

Brandenburg, A., Advances in mean-field dynamo theory and applications to astrophysical turbulence. J. Plasma Phys., 2018, 84, 735840404.

Brandenburg, A., Ambipolar diffusion in large Prandtl number turbulence. Month. Not. Roy. Astron. Soc., 2019a, 487, 2673– 2684.

Brandenburg, A., The Limited Roles of Autocatalysis and Enantiomeric Cross-Inhibition in Achieving Homochirality in Dilute Systems. Origins of Life and Evolution of the Biosphere, 2019b, 49, 49–60.

Brandenburg, A., Hall cascade with fractional magnetic helicity in neutron star crusts. Astrophys. J., 2020a, 901, 18.

Brandenburg, A., Piecewise quadratic growth during the 2019 novel coronavirus epidemic. Infectious Disease Modelling, 2020b, 5, 681–690.

Brandenburg, A., Scientific usage of the Pencil Code., 2020c, DOI:10.5281/zenodo.3466444.

Brandenburg, A., Hosking integral in non-helical Hall cascade. J. Plasma Phys., 2023a, 89, 175890101.

Brandenburg, A., Quadratic growth during the COVID-19 pandemic: merging hotspots and reinfections. J. Phys. A Math., 2023b, 56, 044002.

Brandenburg, A., Ashurova, M.B. and Jabbari, S., Compensating Faraday Depolarization by Magnetic Helicity in the Solar Corona. Astrophys. J., 2017c, 845, L15.

Brandenburg, A. and Banerjee, A., Turbulent magnetic decay controlled by two conserved quantities. arXiv e-prints, 2024, arXiv:2406.11798.

Brandenburg, A. and Boldyrev, S., The Turbulent Stress Spectrum in the Inertial and Subinertial Ranges. Astrophys. J., 2020, 892, 80.

Brandenburg, A., Bracco, A., Kahniashvili, T., Mand al, S., Roper Pol, A., Petrie, G.J.D. and Singh, N.K., E and B Polarizations from Inhomogeneous and Solar Surface Turbulence. Astrophys. J., 2019a, 870, 87.

Brandenburg, A. and Brüggen, M., Hemispheric Handedness in the Galactic Synchrotron Polarization Foreground. Astrophys. J. Lett., 2020, 896, L14.

Brandenburg, A. and Chen, L., The nature of mean-field generation in three classes of optimal dynamos. J. Plasma Phys., 2020, 86, 905860110.

Brandenburg, A., Clarke, E., He, Y. and Kahniashvili, T., Can we observe the QCD phase transition-generated gravitational waves through pulsar timing arrays?. Phys. Rev. D, 2021a, 104, 043513.

Brandenburg, A., Clarke, E., Kahniashvili, T., Long, A.J. and Sun, G., Relic gravitational waves from the chiral plasma instability in the standard cosmological model. Phys. Rev. D, 2024b, 109, 043534.

Brandenburg, A. and Das, U., The time step constraint in radiation hydrodynamics. Geophys. Astrophys. Fluid Dynam., 2020, 114, 162–195.

Brandenburg, A. and Das, U., Turbulent radiative diffusion and turbulent Newtonian cooling. Phys. Fluids, 2021, 33, 095125.

Brandenburg, A., Durrer, R., Huang, Y., Kahniashvili, T., Mandal, S. and Mukohyama, S., Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation. Phys. Rev. D, 2020b, 102, 023536.

Brandenburg, A., Durrer, R., Kahniashvili, T., Mand al, S. and Yin, W.W., Statistical properties of scale-invariant helical magnetic fields and applications to cosmology. J. Cosmol. Astropart. Phys., 2018b, 2018, 034.

Brandenburg, A. and Furuya, R.S., Application of a helicity proxy to edge-on galaxies. Month. Not. Roy. Astron. Soc., 2020, 496, 4749–4759.

Brandenburg, A., Gogoberidze, G., Kahniashvili, T., Mandal, S., Pol, A.R. and Shenoy, N., The scalar, vector, and tensor modes in gravitational wave turbulence simulations. Class. Quantum Grav., 2021b, 38, 145002.

Brandenburg, A., He, Y., Kahniashvili, T., Rheinhardt, M. and Schober, J., Relic Gravitational Waves from the Chiral Magnetic Effect. Astrophys. J., 2021c, 911, 110.

Brandenburg, A., He, Y. and Sharma, R., Simulations of Helical Inflationary Magnetogenesis and Gravitational Waves. Astrophys. J., 2021d, 922, 192.

Brandenburg, A., Iarygina, O., Sfakianakis, E.I. and Sharma, R., Magnetogenesis from axion-SU(2) inflation. J. Cosmol. Astropart. Phys., 2024c, 2024, 057.

Brandenburg, A., Kahniashvili, T., Mandal, S., Pol, A.R., Tevzadze, A.G. and Vachaspati, T., Evolution of hydromagnetic turbulence from the electroweak phase transition. Phys. Rev. D, 2017d, 96, 123528.

Brandenburg, A., Kahniashvili, T., Mandal, S., Pol, A.R., Tevzadze, A.G. and Vachaspati, T., Dynamo effect in decaying helical turbulence. Phys. Rev. Fluids, 2019b, 4, 024608.

Brandenburg, A., Kamada, K., Mukaida, K., Schmitz, K. and Schober, J., Chiral magnetohydrodynamics with zero total chirality. Phys. Rev. D, 2023a, 108, 063529.

Brandenburg, A., Kamada, K. and Schober, J., Decay law of magnetic turbulence with helicity balanced by chiral fermions. Phys. Rev. Res., 2023b, 5, L022028.

Brandenburg, A., Käpylä, P.J., Rogachevskii, I. and Yokoi, N., Helicity Effect on Turbulent Passive and Active Scalar Diffusivities. Astrophys. J., 2025a, 984, 88.

Brandenburg, A. and Larsson, G., Turbulence with Magnetic Helicity That Is Absent on Average. Atmosphere, 2023, 14, 932.

Brandenburg, A., Larsson, G., Del Sordo, F. and Käpylä, P.J., Magnetorotational instability in a solar mean-field dynamo. arXiv e-prints, 2025b, arXiv:2504.16849.

Brandenburg, A. and Ntormousi, E., Dynamo effect in unstirred self-gravitating turbulence. Month. Not. Roy. Astron. Soc., 2022, 513, 2136–2151.

Brandenburg, A. and Ntormousi, E., Magnetic field amplification during a turbulent collapse. arXiv e-prints, 2025, arXiv:2505.02885.

Brandenburg, A. and Protiti, N.N., Electromagnetic Conversion into Kinetic and Thermal Energies. Entropy, 2023, 25, 1270.

Brandenburg, A. and Rempel, M., Reversed Dynamo at Small Scales and Large Magnetic Prandtl Number. Astrophys. J., 2019, 879, 57.

Brandenburg, A., Rogachevskii, I. and Schober, J., Dissipative magnetic structures and scales in small-scale dynamos. Month. Not. Roy. Astron. Soc., 2023c, 518, 6367–6375.

Brandenburg, A. and Scannapieco, E., Magnetic Helicity Dissipation and Production in an Ideal MHD Code. Astrophys. J., 2020, 889, 55.

Brandenburg, A. and Scannapieco, E., Magnetically Assisted Vorticity Production in Decaying Acoustic Turbulence. Astrophys. J., 2025, 983, 105.

Brandenburg, A., Schober, J., Rogachevskii, I., Kahniashvili, T., Boyarsky, A., Fröhlich, J., Ruchayskiy, O. and Kleeorin, N., The Turbulent Chiral Magnetic Cascade in the Early Universe. Astrophys. J., 2017e, 845, L21.

Brandenburg, A. and Sharma, R., Simulating Relic Gravitational Waves from Inflationary Magnetogenesis. Astrophys. J., 2021, 920, 26.

Brandenburg, A., Sharma, R. and Vachaspati, T., Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor. J. Plasma Phys., 2023d, 89, 905890606.

Brandenburg, A. and Vishniac, E.T., Magnetic Helicity Fluxes in Dynamos from Rotating Inhomogeneous Turbulence. Astrophys. J., 2025, 984, 78.

Brandenburg, A., Yi, L. and Wu, X., Inverse cascade from helical and non-helical decaying columnar magnetic fields. J. Plasma Phys., 2025c, 91, E113.

Brandenburg, A., Zhou, H. and Sharma, R., Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos. Month. Not. Roy. Astron. Soc., 2023e, 518, 3312–3325.

Brun, A.S., García, R.A., Houdek, G., Nandy, D. and Pinsonneault, M., The Solar-Stellar Connection. Space Sci. Ref., 2015, 196, 303–356.

Brun, A.S. and Browning, M.K., Magnetism, dynamo action and the solar-stellar connection. Liv. Rev. Solar Phys., 2017, 14, 4.

Bushby, P.J., Käpylä, P.J., Masada, Y., Brandenburg, A., Favier, B., Guervilly, C. and Käpylä, M.J., Large-scale dynamos in rapidly rotating plane layer convection. Astron. Astrophys., 2018, 612, A97.

Bykov, A.M., Brandenburg, A., Malkov, M.A. and Osipov, S.M., Microphysics of Cosmic Ray Driven Plasma Instabilities. Space Sci. Ref., 2013, 178, 201–232.

Cañas, M.H., Lyra, W., Carrera, D., Krapp, L., Sengupta, D., Simon, J.B., Umurhan, O.M., Yang, C.C. and Youdin, A.N., A Solution for the Density Dichotomy Problem of Kuiper Belt Objects with Multispecies Streaming Instability and Pebble Accretion. Planet. Sci. J., 2024, 5, 55.

Cabezón, R.M., García-Senz, D. and Figueira, J., SPHYNX: an accurate density-based SPH method for astrophysical applications. Astron. Astrophys., 2017, 606, A78.

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Cameron, R.H., Dikpati, M. and Brandenburg, A., The Global Solar Dynamo. Space Sci. Ref., 2017, 210, 367–395.

Candelaresi, S. and Beck, C., Twisted magnetic knots and links. Phys. Plasmas, 2023, 30, 082102.

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